This article is cited in 12 papers

A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme

N. V. Timofeeva

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: A new compactification of the variety of moduli of stable vector 2-bundles with Chern classes $c_1$ and $c_2$ is constructed for the case in which the universal family of stable sheaves with given values of invariants is defined and there are no strictly semistable sheaves. The compactification is a subvariety in the Hilbert scheme of subschemes of a Grassmann manifold with fixed Hilbert polynomial; it is obtained from the variety of bundle moduli by adding points corresponding to locally free sheaves on surfaces which are modifications of the initial surface. Moreover, a morphism from the new compactification of the moduli space to its Gieseker–Maruyama compactification is constructed.

Keywords: compactification, moduli space, projective surface, Gieseker stable vector bundle, stable sheaf, Hilbert scheme, universal scheme, Grassmann manifold.

UDC: 512.7

Received: 27.04.2006
Revised: 28.05.2007

DOI: 10.4213/mzm4087

 English version: Mathematical Notes, 2007, 82:5, 677–690

Bibliographic databases:

• 
• 
• 
• 
•