Luca Rizzi, Francesco Zucconi
Using the notion of generalized divisors introduced by Hartshorne, we adapt the theory of adjoint forms to the case of Gorenstein curves. We show an infinitesimal Torelli-type theorem for vector bundles on Gorenstein curves. We also construct explicit counterexamples to the infinitesimal Torelli claim in the case of a reduced reducible Gorenstein curve.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.
We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analogue of Oort's conjecture in the hyperelliptic case.
Moduli of Persson surfaces: The compactification via KSBA stable pairs and a generic global Torelli type theorem
本文研究了由Persson引入的一类canonical polarized表面，这些表面作为Galois覆盖P²的八条一般线的分支。通过构造紧化的模空间，并利用KSBA稳定对描述稳定退化，证明了紧化的模堆光滑。此外，建立了通用的全球Torelli型结果：通过反不变部分的第二上同调群的Hodge结构和相关的G作用，可以恢复大部分Persson表面。
A note on $\mathbb{Q}$-Gorenstein surfaces
本文在代数闭域上构造了一个典范环非有限生成的正规射影$\mathbb{Q}$-Gorenstein曲面，并给出了正特征下$\mathbb{Q}$-Gorenstein曲面极小模型程序的一个反例。
In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside $\mathsf{A}_g$. We describe the second fundamental form of the Torelli map as a multiplication map, recall the relation between totally geodesic subvarieties and Hodge loci and survey various results related to totally geodesic subvarieties and the Jacobian locus.
Rigidity of modular morphisms via Fujita decomposition
本文利用曲线族Hodge丛的Fujita分解性质，证明了Torelli、Prym、Spin-Torelli态射及射影曲线模叠间覆盖映射的刚性，即它们不可形变。
In this note we prove that a conjectural formula for the class $λ_g \mathrm{DR}_g(a,-a)\in R^{2g}(\overline{\mathcal{M}}_{g,2})$ proposed recently by Buryak-Iglesias-Shadrin is true in the Gorenstein quotient of the ring $R^*(\overline{\mathcal{M}}_{g,2})$. As a corollary we prove the strong $\mathrm{DR} \backslash \mathrm{DZ}$ equivalence conjecture for one-point correlators.
The Torelli group $\mathcal T(X)$ of a closed smooth manifold $X$ is the subgroup of the mapping class group $π_0(\mathrm{Diff}^+(X))$ consisting of elements which act trivially on the integral cohomology of $X$. In this note we give counterexamples to Theorem 3.4 of Verbitsky's paper "Mapping class group and a global Torelli theorem for hyperkähler manifolds" (Duke Math.~J.~162 (2013), no.~15, 2929-2986) which states that the Torelli group of simply connected Kähler manifolds of complex dimension $\ge 3$ is finite. This is done by constructing under some mild conditions homomorphisms $J: \mat…
Given a generic curve of genus $g\geqslant4$ and a smooth point $L\in W_{g-1}^{1}(C)$, whose linear system is base-point free, we consider the Abel-Jacobi normal function associated to $L^{\otimes 2}\otimes ω_{C}^{-1}$, when $(C,L)$ varies in moduli. We prove that its infinitesimal invariant reconstruct the couple $(C,L)$. When $g=4$, we obtain the generic Torelli theorem proved by Griffiths.
In this note the geography of minimal surfaces of general type admitting $\mathbb{Z}_2^2$-actions is studied. More precisely, it is shown that Gieseker's moduli space $\mathfrak{M}_{K^2,χ}$ contains surfaces admitting a $\mathbb{Z}_2^2$-action for every admissible pair $(K^2, χ)$ such that $2χ-6\leq K^2\leq 8χ-8$ or $K^2=8χ$. The examples considered allow to prove that the locus of Gorenstein stable surfaces is not closed in the KSBA-compactification $\overline{\mathfrak{M}}_{K^2,χ}$ of Gieseker's moduli space $\mathfrak{M}_{K^2,χ}$ for every admissible pair $(K^2, χ)$ such that $2χ-6\leq K^2\…
This article is motivated by the original Casson invariant regarded as an integral lifting of the Rochlin invariant. We aim to defining an integral lifting of the Adams e-invariant of stably framed 3-manifolds, perhaps endowed with some additional structure. We succeed in doing so for manifolds which are links of normal complex Gorenstein smoothable singularities. These manifolds are naturally equipped with a canonical $\SU$-frame. To start we notice that the set of homotopy classes of $\SU$-frames on the stable tangent bundle of every closed oriented 3-manifold is canonically a $\mathbb Z$-to…
We prove that for a Q-Gorenstein degeneration $X$ of del Pezzo surfaces, the number of non-Du Val singularities is at most $ρ(X)+2$. Degenerations with $ρ(X)+2$ and $ρ(X)+1$ non-Du Val points are investigated.
In these expository notes I discuss several concepts and results in the theory of modules over commutative rings, revolving around the Gorenstein dimension of modules. Some of the related notions are the Auslander dual, k-torsionless modules, and k-th syzygies. Essentially everything in these notes can be found, in one form or another, in the memoir "Stable module theory" by M. Auslander and M. Bridger (Mem. A.M.S., no. 94, 1969). The only difference is in presentation. In the Auslander-Bridger memoir many of the results are proved in the most general setting, e.g. over possibly non-commutativ…
Suppose that $R$ is a ring essentially of finite type over a perfect field of characteristic $p > 0$ and that $a \subseteq R$ is an ideal. We prove that the set of $F$-jumping numbers of $τ_b(R; a^t)$ has no limit points under the assumption that $R$ is normal and $Q$-Gorenstein -- we do \emph{not} assume that the $Q$-Gorenstein index is not divisible by $p$. Furthermore, we also show that the $F$-jumping numbers of $τ_b(R; Δ, a^t)$ are discrete under the more general assumption that $K_R + Δ$ is $\bR$-Cartier.
In this note, we prove effective semi-ampleness conjecture due to Prokhorov and Shokurov for a special case, more concretely, for Q-Gorenstein klt-trivial fibrations over smooth projective curves whose fibers are all klt log Calabi-Yau pairs of Fano type.
We compute orbi-disk invariants of compact Gorenstein semi-Fano toric orbifolds by extending the method used for toric Calabi-Yau orbifolds. As a consequence the orbi-disc potential is analytic over complex numbers.
This note mainly studies the generic finiteness of ϕ_m of a complex projective 3-fold of general type. A new result on the classification to bicanonical pencil for Gorenstein 3-folds is attached in the last section.
The generalized commuting and isospectral commuting varieties of a reductive Lie algebra have been introduced in a preceding article. In this note, it is proved that their normalizations are Gorenstein with rational singularities. Moreover, their canonical modules are free of rank 1. In particular, the usual commuting variety is Gorenstein with rational singularities and its canonical module is free of rank 1.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。