Torsion of a finite base locus

Rémi Bignalet-Cazalet (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We interpret geometrically the torsion of the symmetric algebra of the ideal sheaf of a zero-dimensional scheme Z defined by n + 1 equations in an n-dimensional variety. This leads us to generalise a formula of A.Dimca and S.Papadima in positive characteristic for a rational transformation with finite base locus. Among other applications, we construct an explicit example of a homaloidal curve of degree 5 in characteristic 3, answering negatively a question of A.V.Dória, S.H.Hassanzadeh and A.Simis.

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

Rémi Bignalet-Cazalet. Torsion of a finite base locus. 2018. ⟨hal-01806603⟩