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arXiv · 1806.00856

Torsion of a finite base locus

Rémi Bignalet-Cazalet
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Abstract

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.

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Rémi Bignalet-Cazalet. 2018-06-03. Torsion of a finite base locus. https://arxiv.org/abs/1806.00856

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