6533b870fe1ef96bd12ceddc

RESEARCH PRODUCT

Torsion of a finite base locus

Rémi Bignalet-cazalet

subject

[ MATH ] Mathematics [math][MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC]Mathematics - Algebraic Geometry13D02 14E05 14B05 14H20[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC][MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][MATH] Mathematics [math][MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG][MATH]Mathematics [math]Mathematics - Commutative Algebra[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG][ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]

description

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.D\'oria, S.H.Hassanzadeh and A.Simis.

yearjournalcountryeditionlanguage
2018-06-03
https://hal.archives-ouvertes.fr/hal-01806603/document