Birational classification of moduli spaces of vector bundles over P-2

AH Schofield

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)

Abstract

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 contributionBirational classification of moduli spaces of vector bundles over P-2
Original languageEnglish
Pages (from-to)433 - 448
Number of pages16
JournalIndagationes Mathematicae
Volume12 (3)
DOIs
Publication statusPublished - Sep 2001

Bibliographical note

Publisher: Elsevier Science BV
Other identifier: IDS Number: 511LK

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