On stability of logarithmic tangent sheaves. Symmetric and generic determinants

TL;DR

This paper proves the stability of logarithmic tangent sheaves for certain singular hypersurfaces and applies this to show stability of determinants and symmetric determinants, describing parts of their moduli space.

Contribution

It establishes stability results for logarithmic tangent sheaves of singular hypersurfaces and applies these to determinants and symmetric determinants, expanding understanding of their moduli spaces.

Findings

Logarithmic tangent sheaves are stable for specific singular hypersurfaces.

Determinants and symmetric determinants have stable logarithmic tangent sheaves.

An open dense subset of the moduli space is described.

Abstract

We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric determinants have stable logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space.