Heights and Geometric Invariant Theory

1997/01/29 by Carlo Gasbarri, Gasbarri, Carlo · 1 citation
Mathematics · #14G40 (Primary) 14D25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9701017

openalex publication_date 1997/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a number field, \OK be its ring of integers. We introduce the notion of compactified representation of GL_N(\OK) and, we see how to associate to a hermitian vector bundle \E over \Spec(\OK) and a compactified representation \T, a hermitian tensor bundle \E_T. We can prove then that there exists a lower bound for the heights of points x∈¶(\E_T) with SL_N(K)--semistable generic fibre in terms of the degree of \E and some universal constants depending only on the compactified representation. We give then three applications: a universal lower bound for general flag varieties, an application to the adjoint representation of SL_N(K) and a construction of a height on the moduli space of semistable vector bundles over algebraic curves.

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