arXiv subjects
Publications and source records attributed to Chenglong Yu.
We study compatibility of perverse truncations for morphisms between Ngô fibrations with rationally smooth total spaces. We show that, under an effective rank inequality, equivariant pullbacks preserve the normalized perverse truncations. Applied to the diagonal, this gives multiplicativity of perverse truncations for Hitchin systems with rationally smooth total spaces.
Let $X\subset\mathbb{P}^n_\mathbb{C}$ be a smooth hypersurface of degree $d\ge2$, with $n\ge3$. We prove that an $m$-dimensional integral projective family of lines sweeping a variety of dimension $y$ satisfies $m\le\max\{2y-d-1,n-3\}$. This proves the de Jong-Debarre conjecture for $d\le n$ and the Beheshti-Starr bound for lines on smooth hypersurfaces for $d\ge n+1$.
Visual agents for symbolic graphics reasoning depend on executable world representations, yet continued improvement remains bottlenecked by ambiguous supervision from final renders. Recent agentic systems refine scenes through repeated interaction, but they lack mechanisms to recursively extract actionable evidence from execution traces, overlooking which proposed symbolic edits survived, disappeared, or interfered during program execution. To address this, we propose VETR (Verified Execution Trajectories for Refinement), a framework that enables agentic recursive self-improvement over executable world representations for symbolic graphics reasoning. Within each task, VETR retains aligned program/render records with bounded runtime observations and introduces an execution refiner that compiles observed writes and state changes into constrained alternative programs. The refiner validates their endpoints and preservation conditions against captured runtime state; the ordinary visual verifier then assesses goal relevance. Repair construction makes no additional language-model calls, but can require additional executions. Evaluations on BlenderGym (280 tasks) and BlenderBench (27 released tasks) with GPT-5.6-luna and Qwen3.8-27B show that VETR consistently outperforms existing refinement strategies, including BlenderAlchemy and VIGA. Controlled ablations evaluate the contributions of execution refinement and role-asymmetric evidence organization under fixed generator-interaction caps.
Let $u_k^{(r)}(H,p)$ be the maximum, over all $k$-vertex $r$-uniform hypergraphs $F$, of the absolute difference between the number of induced copies of $F$ in $H$ and its expectation in the binomial random $r$-graph with the same number of vertices as $H$ and edge probability $p$. Let $u_k^{(r)}(n,p)$ be the minimum of $u_k^{(r)}(H,p)$ over all $n$-vertex $r$-uniform hypergraphs, and let $D_r(n,p)$ be the distance from $p\binom nr$ to the nearest integer. For fixed $r\ge3$, $k\ge2r$ and $\varepsilon>0$, the quantity $u_k^{(r)}(n,p)$ has order $\max\!\left\{D_r(n,p),p(1-p)\right\}n^{k-r}$ whenever $p(1-p)n^{\lfloor r/2\rfloor/(\binom{2r-2}{r}-1)}\ge\varepsilon$. Using local moment estimates and switchings in a sparse reservoir, we construct one hypergraph with the nearest-integer edge count that controls all induced orders simultaneously.
Generative recommendation, has been attracted a surge of attentions in industrial and academic research community, towards to build more smart system to build next-generation recommender. Under the significant developing wave of large language model, our team have been developed Semantic ID based OneRec/OneRec-V2. These models have been widely deployed in production and demonstrate the scaling potential of the autoregressive next-item prediction paradigm for industrial recommender systems. Building on the success of OneRec, we further explored a series of models, including OneRec-Think, OpenOneRec, and OneReason, that connect item Semantic IDs with natural language in a unified representation space and seek to unlock the potential of natural-language chain-of-thought (CoT) reasoning for recommendation. However, our preliminary works found that introducing reasoning CoT does not always improve the recommendation performance. To address this issue, OneReason strengthens the semantic alignment between items and language, introduces structured template-based supervision for interest reasoning, and applies advanced reinforcement learning techniques to make reasoning more beneficial to recommendation. As a frontier topic to building recommendation foundation models, we believe this topic has significant research value and hope to encourage more researchers to explore it together. To this end, together with the SIGIR 2026 community, we organized the KUAISHOU Explorer LLM-Rec Challenge 2026: Reasoning Generative Recommendation.
We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. If, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, and the boundary fiber has only isolated singularities whose summed mixed Hodge spectrum is concentrated, then the family is rigid. This includes degenerations with only ordinary double points and cusps. The proof combines a local vanishing-cycle analysis with a global tensor-product decomposition of the associated variation of Hodge structures. We also prove an infinitesimal version. An explicit non-isotrivial, nonrigid family shows that the isolated-singularity assumption alone is insufficient.
We classify commensurability relations between Deligne--Mostow--Thurston monodromy groups and the sixteen arithmetic Ghazouani--Pirio monodromy groups arising from moduli of flat cone metrics on the sphere and on the torus. In both settings, the monodromy group preserves a skew-Hermitian form coming from twisted homology. We use a degeneration method to compute their determinant classes in the genus one case. The defining CM fields and determinant classes of the skew-Hermitian forms determine the commensurability relations. In particular, each of the sixteen arithmetic Ghazouani--Pirio monodromy groups is commensurable with an arithmetic Deligne--Mostow--Thurston monodromy group.
It is an important problem to know whether the monodromy on the cohomology of Milnor fibers associated to hyperplane arrangements is a combinatorial invariant. In this paper, we obtain a combinatorial vanishing criterion for certain eigenspaces of this algebraic monodromy in line arrangements. Combining with Hirzebruch inequality, which is a consequence of Bogomolov--Miyaoka--Yau inequality, we prove that for essential complex line arrangements, the eigenvalues of the monodromy have orders at most five. This is a partial progress toward Papadima--Suciu conjecture and proves Salvetti--Serventi connectivity conjecture. For essential complexified real line arrangements, the monodromy order is improved to at most four thanks to Shnurnikov's inequality. This confirms Papadima--Suciu conjecture for real line arrangements and also Yoshinaga's sharp pair conjecture.
InfRared Small Target Detection (IRSTD) is a challenging task. Relying solely on pixel-level information, vision-only methods struggle to distinguish targets from clutter. Current multimodal methods typically describe both targets and backgrounds with a single textual prompt. Such an approach lacks dedicated regional guidance and ignores infrared semantic asymmetry. Consequently, it provides insufficient background suppression information and introduces severe feature optimization conflicts, overwhelming small targets with noise. To address these issues, we propose a novel Asymmetric Dual-text Guided Network (ADGNet). Specifically, accounting for the infrared semantic asymmetry, we first design the Asymmetric Dual-text Prompt (ADP), comprising an image-agnostic abstract target prompt and an image-specific detailed background prompt. To leverage these prompts, we introduce an Asymmetric Dual-Branch Interaction (ADBI) module to separately guide visual features with their respective text priors, protecting targets from noise while suppressing background clutter. Subsequently, we introduce an Adaptive Feature Aggregation (AFA) module to dynamically fuse features from the two branches. Furthermore, we construct a multimodal Asymmetric Image-Text Infrared (AITIR) dataset by providing asymmetric text annotations for three public datasets (IRSTD-1K, NUDT-SIRST, and SIRST). Extensive experiments demonstrate that ADGNet outperforms 21 state-of-the-art (SOTA) methods. Code is available at https://github.com/iLearn-Lab/MM26-ADGNet.
InfRared Small Target Detection (IRSTD) is a prominent and challenging task in computer vision. In recent years, text-guided methods have significantly improved detection performance. However, they still suffer from two key limitations. First, a single text description simultaneously modeling both background and target leads to semantic entanglement, which contradicts the objective of background suppression and target enhancement. Second, reliance on image-specific textual prompts (requiring additional external models such as CLIP during inference) results in deployment constraints. To address these issues, we propose a novel Dual-knowledge Guided Network (DGNet) based on multiple generalizable texts. Specifically, we design a Prior-knowledge Wavelet Modulation (PWM) module, which leverages dual textual priors that separately characterize large-scale backgrounds and sparse targets to effectively disentangle and modulate entangled semantics in the frequency domain. Furthermore, we introduce a Consensus-knowledge Directional Alignment (CDA) loss, which models the initial state and the ideal target across samples as `complex background' and `bright target', respectively, thereby constructing a clear and unified directional optimization trajectory for the model. Extensive experiments on three public datasets demonstrate the superior performance of DGNet and the effectiveness of each component. The source code is available at https://github.com/iLearn-Lab/MM26-DGNet.
In this paper we mainly study Calabi--Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those families of Calabi--Yau varieties, the period maps factor through arithmetic quotients of complex hyperbolic balls. We give a classification of such examples. One of the families was previously studied by Voisin, Borcea and Rohde. For these ball-type cases, we will show arithmeticity of the monodromy groups. These ball quotients are all commensurable to ball quotients in Deligne--Mostow theory. As a byproduct, we prove some commensurability relations among arithmetic groups in Deligne--Mostow theory.
We propose a log-concavity conjecture for BPS invariants arising in the enumerative geometry of planar curve singularities, identified with the local Euler obstructions of Severi strata in their versal deformations. We further extend this conjecture to ruling polynomials of Legendrian links and to E-polynomials of character varieties. We establish these conjectures for irreducible weighted-homogeneous singularities (torus knots) and for ADE singularities, and prove a multiplicative property for ruling polynomials compatible with log-concavity.
We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga.
The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric functions using Deligne--Mostow theory and the geometric correspondence between curves and surfaces. In this paper, we apply the same construction to obtain transformation formulas among these hypergeometric functions. This also provides an alternative approach to some of Goursat's quadratic transformations via double integrals and Fubini's theorem.
This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Mustaţă and Teitler and implies the strong topological monodromy conjecture for arrangements. Walther gave a sufficient condition that a certain differential form does not vanish in the top cohomology group of Milnor fiber. We use Walther's result to verify the $n\over d$-conjecture for weighted hyperplane arrangements satisfying the nonresonant condition.
In this paper, we study moduli spaces of sextic curves with simple singularities. Through period maps of K3 surfaces with ADE singularities, we prove that such moduli spaces admit algebraic open embeddings into arithmetic quotients of type IV domains. For all cases, we prove the identifications of GIT compactifications and Looijenga compactifications. We also describe Picard lattices in an explicit way for many cases. For nodal cases, we prove that the orbifold structures on the two sides of the period map are isomorphic.
This paper gives the commensurability classification of Deligne--Mostow ball quotients and shows that the 104 Deligne--Mostow lattices form 38 commensurability classes. First, we find commensurability relations among Deligne--Mostow monodromy groups, which are not necessarily discrete. This generalizes previous work by Sauter and Deligne--Mostow in dimension two. In this part, we consider certain projective surfaces with two fibrations over the projective line, which induce two sets of Deligne--Mostow data. Correspondences between moduli spaces provide a geometric realization of commensurability relations. Secondly, we obtain commensurability invariants from conformal classes of Hermitian forms and toroidal boundary divisors. This completes the commensurability classification of Deligne--Mostow lattices and provides an alternative approach to the results of Kappes--M{ö}ller and McMullen on non-arithmetic Deligne--Mostow lattices.
In this paper we study the moduli spaces of nodal sextic curves. We realize each irreducible component of the GIT space of sextic curves with given number of nodes as an open subspace of type IV arithmetic quotients. We then focus on the compactifications of the moduli spaces, one side is the geometric (GIT) compactifications, the other side is the Hodge theoretic compactifications such as Looijenga compactifications and Baily--Borel compactifications. The main result is the isomorphism between GIT and Looijenga compactifications. Some examples are closely related to del Pezzo surfaces. We also extend our results to moduli of nodal sextic curves with specified symmetry.