Birational classification of moduli spaces of vector bundles over $\mathbb{P}^{2}$

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dc.creatorSchofield, Aidan
dc.date1999-12-01
dc.date.accessioned2026-07-07T05:32:03Z
dc.date.available2026-07-07T05:32:03Z
dc.descriptionThe depth of a vector bundle E over the projective plane 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 <= 4 and is stably rational when h divides 420.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/9912005
dc.identifierhttp://arxiv.org/abs/math/9912005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79523
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14J60 (Primary) 16G20 (Secondary)
dc.titleBirational classification of moduli spaces of vector bundles over $\mathbb{P}^{2}$
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