Witten's top Chern class via K-theory

Details Witten's top Chern class via K-theory Witten's top Chern class via K-theory

2002-10-25

arxiv.org/abs/math/0210398v2

Mathematics

Algebraic Geometry

25 pages, revised version, to appear in J. Algebraic Geom

Scientific paper

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.

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