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 language | English |
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Pages (from-to) | 367-377 |
Number of pages | 11 |
Journal | International Mathematics Research Notices |
Volume | 2020 |
Issue number | 2 |
DOIs | |
Publication status | Published - 20 Jan 2020 |
Funding
This work was supported by the Chinese National Science Foundation to [E.L.]