Discriminants of morphisms of sheaves

Helge Øystein Maakestad

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arXiv · 0911.4804

Discriminants of morphisms of sheaves

Helge Øystein Maakestad

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Abstract

The aim of this paper is to give a unified definition of a large class of discriminants arising in algebraic geometry using the discriminant of a morphism of locally free sheaves. The discriminant of a morphism of locally free sheaves has a geometric definition in terms of grassmannian bundles, tautological sequences and projections and is a simultaneous generalization of the discriminant of a morphism of schemes, the discriminant of a linear system on a smooth projective scheme and the classical discriminant of degree $d$ polynomials. We study the discriminant of a morphism in various situations: The discriminant of a finite morphism of schemes, the discriminant of a linear system on the projective line and the discriminant of a linear system on a flag variety. The main result of the paper is that the discrimiant of any linear system on any flag variety is irreducible.

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BibTeX RIS

Helge Øystein Maakestad. 2009-11-25. Discriminants of morphisms of sheaves. https://arxiv.org/abs/0911.4804

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