Article
Licensed
Unlicensed
Requires Authentication
Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
-
Markus Dürr
Published/Copyright:
January 30, 2009
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].
Received: 2007-06-11
Published Online: 2009-01-30
Published in Print: 2009-May
© de Gruyter 2009
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
