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DTSTART;TZID=Asia/Seoul:20230425T110000
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SUMMARY:Junyan Zhao\, Moduli of Curves of Genus 6 and K-stability
DESCRIPTION:    Speaker\n\n\nJunyan Zhao\nUniversity of Illinois Chicago\n\n\n\n\n\n\nA general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X5 as a divisor of class -2KX5. This embedding is unique up to the action of the symmetric group S5. Taking a double cover of X5 branched along C yields a K3 surface Y. Thus the K-moduli spaces of the pair (X5\, C) can be studied via wall-crossing and by relating them to the Hassett-Keel program for C and the HKL program for Y. On the other hand\, X5 can be embedded in P1 × P2 as a divisor of class O(1\,2)\, under which -2KX is linearly equivalent to OX(2\,2). One can study the VGIT-moduli spaces in this setting. In this talk\, I will compare these four types of compactified moduli spaces and their different birational models given by wall-crossing.
URL:https://ccg.ibs.re.kr/event/2023-04-25/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
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