Deformations of the Fano scheme of a cubic

2022/07/18 by Stark, Samuel
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.08762

Abstract

We study the deformation theory of the Fano scheme F=F(X) of lines on a cubic X of dimension d with only finitely many singularities. By taking the relative Fano scheme, we define a morphism η:\mathscrD_X→\mathscrD_F of the local moduli functors associated to X and F, respectively. We show that for d\geqslant 5, η yields an isomorphism on first-order deformations; in particular, η is an isomorphism whenever H⁰(Θ_X)=0.

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