In:
advg, Walter de Gruyter GmbH, Vol. 9, No. 2 ( 2009-05), p. 219-231
Abstract:
In [Dürr, Kabanov, Okonek, Topology 46: 225–294, 2007] we constructed virtual fundamental classes for Hilbert schemes of divisors of topological type m on a surface V , and used these classes to define the Poincaré invariant of V : We conjecture that this invariant coincides with the full Seiberg–Witten invariant computed with respect to the canonical orientation data. In this note we prove that the existence of an integral curve C ⊂ V induces relations between some of these virtual fundamental classes . The corresponding relations for the Poincaré invariant can be considered as algebraic analoga of the fundamental relations obtained in [Ozsváth, Szabó, Ann. of Math. 151: 93–124, 2000].
Type of Medium:
Online Resource
ISSN:
1615-7168
,
1615-715X
DOI:
10.1515/ADVGEOM.2009.014
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2009
detail.hit.zdb_id:
2043066-8
SSG:
17,1