Deforming a canonical curve inside a quadric

2017/02/02 by Marco Boggi, Boggi, Marco, Eduard Looijenga +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1702.00770

6 pages

arxiv created 2017/02/02 · arxiv updated 2017/02/03

Abstract

Let C⊂\mathbb P^g-1 be a canonically embedded nonsingular nonhyperelliptic curve of genus g and let X⊂\mathbb P^g-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. As we will show in a forthcoming paper, this has applications of a topological nature.

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