Cokernel bundles and Fibonacci bundles

Abstract

Abstract. We are interested in those bundles C on P N which admit a resolution of the formIn this paper we prove that, under suitable conditions on (E, F ), a generic bundle with this form is either simple or canonically decomposable. As applications we provide an easy criterion for the stability of such bundles on P 2 and we prove the stability when E = O, F = O(1) and C is an exceptional bundle on P N for N ≥ 2.

The stability of exceptional bundles on complete intersection 3-folds

“…In [6], Drézet and Le Potier prove that any exceptional bundle on P 2 is stable. The stability of exceptional bundles on the quadric P 1 × P 1 is proved by Gorodentsev in [7], and the stability of exceptional Steiner bundles on P n , n ≥ 2, and on the hyperquadric Q n ⊂ P n+1 , n ≥ 3, is proved in [1] and [13], respectively. In [14], Zube proves that any exceptional bundle on K3 surfaces with Picard group Z is stable and uses this result to prove that exceptional bundles on P 3 are stable.…”

Cohomological characterisation of Steiner bundles

“…These bundles had been considered earlier by others (see [17], [5]) and, after [16], they have been studied by many authors such as Vallès [38,39], Ancona and Ottaviani [1], Cascini [9], Brambilla [7,6], Jardim and Martins [25] and also by us. More precisely, in [36] we defined and studied Steiner bundles on the smooth hyperquadric Q n ⊂ P n+1 .…”

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.…”

“…Fibonacci bundles on P n have been recently introduced in [4] as a generalization of the Steiner exceptional bundles, namely of the exceptional bundles which admit a linear resolution. Fibonacci bundles are homogeneous and generated by mutations.…”

“…In Section 4, we deal with the G-exceptionality of these bundles, proving that any almost square bundle on P 2 is simple and that any Fibonacci bundle is G-exceptional. In the proof we use cohomological methods, inspired by [4]. Section 5 is devoted entirely to prove that any almost square bundle on P 2 is stable.…”