Stable rationality of Brauer–Severi surface bundles

Stable Rationality and Conic Bundles

We study stable rationality properties of conic bundles over rational surfaces.

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 .

On the Rationality of Certain Strata of the Lange Stratification of Stable Vector Bundles on Curves

Let X be a smooth projective curve of genus g ≥ 2 and S(r, d) the moduli scheme of all rank r stable vector bundles of degree d on X. Fix an integer k with 0 < k < r. H. Lange introduced a natural stratification of S(r, d) using the degree of a rank k subbundle of any E ∈ S(r, d) with maximal degree. Every non-dense stratum, say W (k, r − k, a, d − a), has in a natural way a fiber structure h :...

Rationality of Moduli Spaces of Parabolic Bundles

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows that if rank and degree are coprime, the moduli space of vector bundles is stably rational, and the bound obtained on the level is strong enough to conclude r...

Stable Extensions by Line Bundles