arXiv subjects

Hongmiao Yu

Publications and source records attributed to Hongmiao Yu.

8 recordsLinked to original sources

arXiv2026

From MHV Gravity Amplitudes and Hodges map to Pentad Varieties

We study some geometric aspects behind the Hodges matrix appearing in the context of scattering amplitudes for the $\mathcal N=8$ supergravity. Through a vector bundle construction, we show that the Hodges matrix gives rise to a canonical rational map from the two-step flag variety to symmetric matrices, called the $\textit{Hodges map}$. This construction allows to define the amplitude geometrically: its vanishing locus is a divisor - the $\textit{MHV gravity divisor}$. Inspired by the Hodges map, we introduce the notion of Hadamard ratio of two varieties. In the case relevant to gravity, this is the ratio of two Grassmannians, which we call the $\textit{pentad variety}$, connecting it to the pentad constraint from algebraic statistics. Moreover, we show that the pentad variety is closely related to the combinatorial algebraic geometry of Martin's affine slope variety, and the phirotopes of Below, Krummeck, and Richter-Gebert.

math.AG↗

arXiv2026

Segre determinants and MHV gravity amplitudes

We describe a Segre-Veronese construction of polynomial solutions to the interpolation conditions of the numerators of tree-level MHV gravity amplitudes given by Hodges' formula. The five- and six-point Hodges numerators arise from Segre determinants, while for every $n\geq7$ suitable Segre determinants lead to solutions linearly independent of the Hodges numerator. The existence of such independent elements for $n=7,8$ was recently established by Mai and Zhang.

hep-th↗

arXiv2026

ABEAT: Efficient and Anonymous Encryption for ABE-based Dynamic Group Communication

Confidential communication among a dynamic group of participants that ensures flexible and efficient many-to- many communication is highly desired capability. We leverage attribute-based encryption (ABE) for confidential group communication and enhance it by a graph-based namespace to create an efficient framework that allows groups to be formed and changed dynamically. In this paper, we focus on the important additional need to maintain the anonymity of recipients of a message, when using ABE for group communication for a variety of usage scenarios (e.g., emergency response). We propose ABEAT, an efficient and anonymous dynamic group communication system that also minimizes overhead on receivers who are not the intended recipients of a message. In ABEAT, we propose a new anonymous KP-ABE approach to maintain recipient anonymity. ABEAT hides the clear attribute in the ciphertext of KP-ABE, and also prevents several attacks that seek to break anonymity. ABEAT provides fast recipient verification, dramatically lowering the decryption overhead for non-recipients by more than a factor of 90 versus the current state of the art such as hidden vector encryption (HVE). In fact, it is even 40% less than FABEO, which offers no anonymity.

cs.CR↗

arXiv2026

On the weak and strong Lefschetz properties for initial ideals of determinantal ideals with respect to diagonal monomial orders

We study the weak and strong Lefschetz properties for $R/\mathrm{in}(I_t)$, where $I_t$ is the ideal of a polynomial ring $R$ generated by the $t$-minors of an $m\times n$ matrix of indeterminates, and $\mathrm{in}(I_t)$ denotes the initial ideal of $I_t$ with respect to a diagonal monomial order. We show that when $I_t$ is generated by maximal minors (that is, $t=\mathrm{min}\{m,n\}$), the ring $R/\mathrm{in}(I_t)$ has the strong Lefschetz property for all $m$, $n$. In contrast, for $t<\mathrm{min}\{m,n\}$, we provide a bound such that $R/\mathrm{in}(I_t)$ fails to satisfy the weak Lefschetz property whenever the product $mn$ exceeds this bound. As an application, we present counterexamples that provide a negative answer to a question posed by Murai regarding the preservation of Lefschetz properties under square-free Gröbner degenerations.

math.AC↗

arXiv2025

A Uniform Identification of Stable Sheaf Cohomology

This paper considers generalizations of certain arithmetic complexes appearing in the work of Raicu and VandeBogert in connection with the study of stable sheaf cohomology on flag varieties. Defined over the ring of integer valued polynomials, we prove an isomorphism of these complexes as conjectured by Gao, Raicu, and VandeBogert. In particular, this shows that a previously made identification between the stable sheaf cohomology of hook and two column partition Schur functors applied to the cotangent sheaf of projective space can be made to be uniform with respect to these complexes. These results are extended to the projective space defined over the integers.

math.AC↗

arXiv2024

Lefschetz duality for local cohomology

Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic features of linked varieties. In this paper we develop a liaison theory via quasi-Gorenstein varieties, a much broader class than Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings are to Gorenstein rings as manifolds are to spheres. As applications, we derive a connectedness property of quasi-Gorenstein subspace arrangements generalizing previous results by Benedetti and the second author, and we deduce the classical topological Lefschetz duality via the Stanley-Reisner correspondence.

math.AC↗

arXiv2023

Componentwise Linearity Under Square-Free Gröbner Degenerations

Using the recent results on square-free Gröbner degenerations by Conca and Varbaro, we proved that if a homogeneous ideal $I$ of a polynomial ring is such that its initial ideal $\mathrm{in}_<(I)$ is square-free and $β_0(I) = β_0(\mathrm{in}_<(I))$, then $I$ is a componentwise linear ideal if and only if $\mathrm{in}_<(I)$ is a componentwise linear ideal. In particular, if furthermore one of $I$ and $\mathrm{in}_<(I)$ is componentwise linear, then their graded Betti numbers coincide.

math.AC↗

arXiv2022

N-fiber-full modules

Let $A$ be a Noetherian flat $K[t]$-algebra, $h$ an integer and let $N$ be a graded $K[t]$-module, we introduce and study "$N$-fiber-full up to $h$" $A$-modules. We prove that an $A$-module $M$ is $N$-fiber-full up to $h$ if and only if $\mathrm{Ext}^i_A(M, N)$ is flat over $K[t]$ for all $i\le h-1$. And we show some applications of this result extending the recent result on squarefree Gröbner degenerations by Conca and Varbaro.

math.AC↗