Group action on instanton bundles over \PP³

2001/03/13 by Laura Costa, Giorgio Ottaviani, Costa, Laura +1
Computer Science · Mathematics · #14F05 #14J60 #14L30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation #math.AG #msc:14F05 #msc:14J60 #msc:14L30

paper · pdf · doi:10.48550/arxiv.math/0103076

24 pages

arxiv created 2001/03/13 · openalex publication_date 2001/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by MI(k) the moduli space of k-instanton bundles E of rank 2 on \PP³=\PP(V) and by Z_k(E) the scheme of k-jumping lines. We prove that [E]∈ MI(k) is not stable for the action of SL(V) if Z_k(E)≠∅. Moreover dim Sym(E)≥ 1 if length Z_k(E)≥ 2. We prove also that E is special if and only if Z_k(E) is a smooth conic. The action of SL(V) on the moduli of special instanton bundles is studied in detail.

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