Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.20011

On deformations of foliated complex analytic structures III: Unfoldings

Chunghoon Kim
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We prove theorem of existence for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves for one-parameter families. We prove theorem of completeness for unfoldings of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also present unfoldings of foliated nonsingular varieties defined by locally free subsheaves of cotangent sheaves in the language of functors of Artin rings which is the algebraic version of unfoldings of foliated complex analytic structures. We identify first-order unfoldings and obstructions.

Explore related subjects

math.AGmath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Chunghoon Kim. 2026-10-14. On deformations of foliated complex analytic structures III: Unfoldings. https://arxiv.org/abs/2610.20011

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Kawamata boundedness for Fano threefolds and the Graded Ring Database

We give an effective realisation of Kawamata's famous bound for Fano 3-folds. Our result is a list of 39,550 candidate Hilbert series $P$ for Fano 3-folds satisfying the Bogomolov stability inequality. For each $P$, there may or may not be a Fano 3-fold $X$ that realises $P$, but even so we give a set of weights that we expect to be among those of a minimal generating set of the anticanonical ring of any such $X$. This provides a crude first approximation to the ongoing classification of Fano 3-folds. We explain in detail what this data means, the important nuances that current known examples reveal about it, and how it relates to a range of different classification programmes.

math.AG↗
arXiv2026

Irreducibility of Some Quot Schemes on Nodal Curves

Let $C$ be an integral projective nodal curve over $\mathbb C$, of arithmetic genus $g \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree $e$. Let $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. We show that $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ is irreducible for $d \gg 0$.

math.AG↗
arXiv2026

Weak del Pezzo surfaces are characterized by the existence of $2$-tilting bundles

For $d\geq1$, a tilting bundle on a regular proper $d$-dimensional variety over a field is called $d$-tilting if its endomorphism algebra has global dimension $d$, the smallest possible value. We prove that, over any field, the existence of a $d$-tilting bundle implies that the anticanonical bundle is semiample and big, and hence the variety is weak Fano. Moreover, the endomorphism algebra is $d$-representation tame. Conversely, every weak del Pezzo surface over an algebraically closed field of arbitrary characteristic admits a $2$-tilting bundle. Thus a smooth projective surface over such a field admits a $2$-tilting bundle if and only if it is a weak del Pezzo surface. This proves the variety case of Chan's conjecture, originally formulated in characteristic zero, and extends it to arbitrary characteristic. As an application, we construct a non-commutative crepant resolution (NCCR) of the anticanonical ring of any regular proper $d$-dimensional variety over any field admitting a $d$-tilting bundle. The NCCR is the endomorphism algebra of the pulled-back bundle on the total space of the canonical bundle. In particular, we obtain NCCRs of anticanonical cones over Du Val del Pezzo surfaces over algebraically closed fields of arbitrary characteristic. These NCCRs are the $3$-Calabi--Yau completions of the endomorphism algebras of $2$-tilting bundles on the minimal resolutions, extending the known construction for smooth del Pezzo surfaces to the Du Val case.

math.AG↗