Stability of 2nd hilbert points of canonical curves

Maksym Fedorchuk; David Jensen

doi:10.1093/imrn/rns204

Stability of 2nd hilbert points of canonical curves

Maksym Fedorchuk, David Jensen

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We establish Geometric Invariant Theory (GIT) semistability of the 2nd Hilbert point of every Gieseker-Petri general canonical curve by a simple geometric argument. As a consequence, we obtain an upper bound on slopes of general families of Gorenstein curves. We also explore the question of what replaces hyperelliptic curves in GIT quotients of the Hilbert scheme of canonical curves.

Original language	English
Pages (from-to)	5270-5287
Number of pages	18
Journal	International Mathematics Research Notices
Volume	2013
Issue number	22
DOIs	https://doi.org/10.1093/imrn/rns204
State	Published - Jan 1 2013

ASJC Scopus subject areas

General Mathematics

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AB - We establish Geometric Invariant Theory (GIT) semistability of the 2nd Hilbert point of every Gieseker-Petri general canonical curve by a simple geometric argument. As a consequence, we obtain an upper bound on slopes of general families of Gorenstein curves. We also explore the question of what replaces hyperelliptic curves in GIT quotients of the Hilbert scheme of canonical curves.

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JO - International Mathematics Research Notices

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Stability of 2nd hilbert points of canonical curves

Abstract

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