A remark on K\"ahler forms on symmetric products of Riemann surfaces

Tim Perutz

A remark on K\"ahler forms on symmetric products of Riemann surfaces

Symplectic Geometry 2008-02-27 v2

Authors: Tim Perutz

Abstract

Users of Heegaard Floer homology may be reassured to know that it can be made to conform exactly to the standard analytic pattern of Lagrangian Floer homology. This follows from the following remark, which we prove using an argument of J. Varouchas: the natural singular K\"ahler form $\sym^n(\omega)$ on the $n$ th symmetric product of a K\"ahler curve $(\Sigma,\omega)$ admits a cohomologous smoothing to a K\"ahler form which equals $\sym^n(\omega)$ away from a chosen neighbourhood of the diagonal.

Keywords

kahler forms symmetric products riemann surfaces heegaard floer homology lagrangian floer homology cohomologous smoothing

Cite

@article{arxiv.math/0501547,
  title  = {A remark on K\"ahler forms on symmetric products of Riemann surfaces},
  author = {Tim Perutz},
  journal= {arXiv preprint arXiv:math/0501547},
  year   = {2008}
}

Comments

4 pages. I have appended this unpublished note to arXiv:0801.0564 (accepted for publication in Proc. 14th Gokova Geometry-Topology conference) - please reference the latter

A remark on K\"ahler forms on symmetric products of Riemann surfaces

Abstract

Keywords

Cite

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