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DTSTART;TZID=Asia/Seoul:20250403T110000
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SUMMARY:Jinhyung Park\, Effective gonality theorem on weight-one syzygies of algebraic curves
DESCRIPTION:    Speaker\n\n\nJinhyung Park\nKAIST\n\n\n\n\n\n\nIn 1986\, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality gon(C) of a smooth projective curve C of genus g can be read off from weight-one syzygies of a sufficiently positive line bundle L\, and also proposed possible least degree of L\, that is 2g+gon(C)-1. In 2015\, Ein-Lazarsfeld proved the conjecture when deg(L) is sufficiently large\, but the effective part of the conjecture remained widely open and was reformulated explicitly by Farkas-Kemeny a few years ago. We show an effective vanishing theorem for weight-one syzygies\, which implies that the gonality conjecture holds if deg(L) is at least 2g+gon(C) or equal to 2g+gon(C)-1 and C is not a plane curve. As Castryck observed that the gonality conjecture may not hold for a plane curve when deg(L)=2g+gon(C)-1\, this result is the best possible and thus gives a complete answer to the gonality conjecture. This is joint work with Wenbo Niu.
URL:https://ccg.ibs.re.kr/event/2025-0403/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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