Speaker: Fei Yu (Zhejiang University)
Abstract: Given a holomorphic differential on a smooth complex algebraic curve, we associate to it a Gorenstein curve singularity with G_m action via a test configuration. This construction decomposes the strata of holomorphic differentials with prescribed orders of zeros into negatively graded versal deformation spaces of such singularities, refining Pinkham’s correspondence between monomial curve singularities and Weierstrass semigroups to the case of Gorenstein singularities with multiple branches in the framework of Looijenga’s deformations with good Gm-action. Our construction provides a uniform approach to describe the resulting singularities and their invariants, such as weights and characters, initially studied by Alper–Fedorchuk–Smyth. As an application, we classify the unique Gorenstein singularity with Gm-action for each nonvarying stratum of holomorphic differentials and hyperelliptic locus, identify each nonvarying stratum with the locus of smooth deformations of the corresponding singularity, and study when these nonvarying strata can be compactified by weighted projective spaces. Additionally, we classify such singularities with bounded α-invariants in the Hassett–Keel log minimal model program for M_g. We also study the slopes of these singularities and utilize them to bound the slopes of effective divisors in M_g. This is a collaborative work Dawei Chen. arxiv:2507.09078v1
Time: 2025-09-26 11:00:00
Location: R1710, SIMIS
Zoom Meeting ID: 844 0594 7424 (Passcode 076895)
Introduction to the speaker: Professor Fei Yu works at Zhejiang University, working on Algebraic Geometry, Dynamical Systems, and their intersections. He is an expert on the deep connection between the dynamics possible on a given surface, and its topology.
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