The stability of exceptional bundles on complete intersection 3-folds

Abstract

Abstract. A very long-standing problem in Algebraic Geometry is to determine the stability of exceptional vector bundles on smooth projective varieties. In this paper we address this problem and we prove that any exceptional vector bundle on a smooth complete intersection 3-fold Y ⊂ P n of type (d 1 , . . . , d n−3 ) with d 1 + · · · + d n−3 ≤ n and n ≥ 4 is stable.

Virtual classes and virtual motives of Quot schemes on threefolds

“…This fact is used in [33] to prove that any exceptional bundle on P 3 is stable. Miró-Roig and Soares [24] prove that if Y ⊂ P n is a smooth complete intersection 3-fold of type (d 1 , . .…”

Simple Helices on Fano Threefolds

“…Remark In the particular case when a Fano threefold is a complete intersection in the projective space, the stability of exceptional vector bundles on X was proved in [15] (also using Zube's trick).…”

G-exceptional vector bundles on P2 and representations of quivers

“…See also [4,14,22] for other families of exceptional vector bundles which are known to be stable. Nevertheless, the stability of exceptional vector bundles on P n and more in general on an algebraic variety X is still an open and difficult problem.…”