Group action on instanton bundles over $\PP^3$

Laura Costa; Giorgio Ottaviani

paper

Group action on instanton bundles over $\PP^3$

arXiv:math/0103076

Abstract

Denote by MI(k) the moduli space of k-instanton bundles E of rank 2 on $\PP^3=\PP(V)$ and by $Z_{k} (E)$ the scheme of k-jumping lines. We prove that $[E] \in M I (k)$ is not stable for the action of SL(V) if $Z_{k} (E) \neq = \emptyset$ . Moreover $dim S y m (E) \geq 1$ if $l e n g t h Z_{k} (E) \geq 2$ . 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.

24 pages