Geometry of symmetric determinantal loci

Abstract

We study algebro-geometric properties of determinantal loci of (n+1)th symmetric matrices and also their double covers for even ranks. Their singularities, Fano indices and birational geometries are studied in general. The double covers of symmetric determinantal loci of rank four are studied with special interest by noting their relation to the Hilbert schemes of conics on Grassmannians.

We have reorganized our paper arXiv:1302.5881. This paper contains generalizations of the first part of that paper

References in corpus (4)

• Semiorthogonal decompositions in algebraic geometry
• Homological projective duality for Grassmannians of lines
• Double quintic symmetroids, Reye congruences, and their derived equivalence
• Duality between S^2 P^4 and the Double Quintic Symmetroid

Cited by in corpus (3)

• On the Hessian of cubic hypersurfaces
• Towards Homological Projective duality for S^2 P^3 and S^2 P^4
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM