On stability of logarithmic tangent sheaves. Symmetric and generic determinants

Daniele Faenzi (1) , Simone Marchesi (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Facultat de Matematiques, Universitat de Barcelona

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.

Mots clés: Logarithmic tangent; stability of sheaves; moduli space of semistable sheaves; isolated singularities; determinant

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Daniele Faenzi, Simone Marchesi. On stability of logarithmic tangent sheaves. Symmetric and generic determinants. 2021. ⟨hal-03112212v1⟩