English

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

R2 v1 2026-07-22T16:48:45.797Z