Double lines on quadric hypersurfaces

TL;DR

This paper investigates the geometry of double line structures and the moduli of stable sheaves on smooth quadric threefolds, focusing on the Hilbert scheme components of curves.

Contribution

It provides new insights into the structure and classification of double lines and stable sheaves on quadric threefolds, expanding understanding of their geometric properties.

Findings

Characterization of irreducible components of the Hilbert scheme

Description of the moduli space of stable sheaves of pure dimension 1

Analysis of the geometry of double line structures

Abstract

We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.