Deforming a Canonical Curve Inside a Quadric

Marco Boggi*, Eduard Looijenga

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Let C ⊂ ℙg-1 be a canonically embedded nonsingular nonhyperelliptic curve of genus g and let X ⊂ ℙg-1 be a quadric containing C. Our main result states among other things that the Hilbert scheme of X is at [C ⊂ X] a local complete intersection of dimension g2 - 1 and is smooth when X is. It also includes the assertion that the minimal obstruction space for this deformation problem is in fact the full associated Ext1-group and that in particular the deformations of C in X are obstructed in case C meets the singular locus of X. Applications will be given in a forthcoming paper.

Original languageEnglish
Pages (from-to)367-377
Number of pages11
JournalInternational Mathematics Research Notices
Volume2020
Issue number2
DOIs
Publication statusPublished - 20 Jan 2020

Funding

This work was supported by the Chinese National Science Foundation to [E.L.]

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