The depth of a vector bundle E over P-2 is the largest integer h such that [E]/h is in the Grothendieck group of coherent sheaves on P-2 where [E] is the class of E in this Grothendieck group. We show that a moduli space of vector bundles is birational to a suitable number of h by h matrices up to simultaneous conjugacy where h is the depth of the vector bundles classified by the moduli space. In particular, such a moduli space is a rational variety if h less than or equal to 4 and is stably rational when h divides 420.
|Translated title of the contribution||Birational classification of moduli spaces of vector bundles over P-2|
|Pages (from-to)||433 - 448|
|Number of pages||16|
|Publication status||Published - Sep 2001|
Bibliographical notePublisher: Elsevier Science BV
Other identifier: IDS Number: 511LK