Witten's top Chern class via K-theory
Algebraic Geometry
2007-05-23 v2
Abstract
The Witten top Chern class is the crucial cohomology class needed to state a conjecture by Witten relating the Gelfand-Dikii hierarchies to higher spin curves. In math.AG/0011032, Polishchuk and Vaintrob provide an algebraic construction of such a class. We present a more straightforward construction via K-theory. In this way we short-circuit the passage through bivariant intersection theory and the use of MacPherson's graph construction. Furthermore, we show that the Witten top Chern class admits a natural lifting to the K-theory ring.
Keywords
Cite
@article{arxiv.math/0210398,
title = {Witten's top Chern class via K-theory},
author = {Alessandro Chiodo},
journal= {arXiv preprint arXiv:math/0210398},
year = {2007}
}
Comments
25 pages, revised version, to appear in J. Algebraic Geom