Stable extensions by line bundles

Stable Extensions by Line Bundles

Extensions of Vector Bundles and Rationality of Certain Moduli Spaces of Stable Bundles

In this paper, it is proved that certain stable rank-3 vector bundles can be written as extensions of line bundles and stable rank-2 bundles. As an application, we show the rationality of certain moduli spaces of stable rank-3 bundles over the projective plane P 2 .

Extensions of Line Bundles and Brill–noether Loci of Rank-two Vector Bundles on a General Curve

In this paper we study Brill-Noether loci for rank-two vector bundles and describe the general member of some components as suitable extensions of line bundles.

Divisors and Line Bundles

An analytic hypersurface of M is a subset V ⊂ M such that for each point x ∈ V there exists an open set Ux ⊂ M containing x and a holomorphic function fx defined on Ux such that V ⊂ Ux is the zero-set of fx. Such an fx is called a local defining function for V near x. The quotient of any two local defining functions around x is a non-vanishing holomorphic function around x. An analytic hypersur...

Volumes of Line Bundles

In this note we describe the asymptotic growth of the number of global sections of line bundles on surfaces. Beside working out concrete examples, we also show that this quantity does not change in a locally polynomial manner on threefolds. 1991 MSC classification: 14C40 (primary), 14J05, 32C10 (secondary)