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arXiv:math/0210398 [math.AG]AbstractReferencesReviewsResources

Witten's top Chern class via K-theory

Alessandro Chiodo

Published 2002-10-25, updated 2006-03-31Version 2

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.

Comments: 25 pages, revised version, to appear in J. Algebraic Geom
Categories: math.AG
Subjects: 14H60, 14H10
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