Discriminants of morphisms of sheaves
Helge {\O}ystein Maakestad

TL;DR
This paper introduces a unified geometric framework for defining and analyzing discriminants of morphisms of sheaves in algebraic geometry, generalizing classical concepts and establishing irreducibility results.
Contribution
It provides a comprehensive geometric definition of discriminants for morphisms of locally free sheaves, extending classical discriminants to broader contexts including flag varieties.
Findings
Discriminant of any linear system on a flag variety is irreducible.
Unified geometric definition encompasses various classical discriminants.
Analysis of discriminants in multiple geometric situations.
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 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications
