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Invariance of tautological equations I: conjectures and applications

Y.-P. Lee (2008)

Journal of the European Mathematical Society

The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to...

Invariante Divisoren und Schnitthomologie von torischen Varietäten

Gottfried Barthel, Jean-Paul Brasselet, Karl-Heinz Fieseler, Ludger Kaup (1996)

Banach Center Publications

In this article, we complete the interpretation of groups of classes of invariant divisors on a complex toric variety X of dimension n in terms of suitable (co-) homology groups. In [BBFK], we proved the following result (see Satz 1 below): Let C l D i v C ( X ) and C l D i v W ( X ) denote the groups of classes of invariant Cartier resp. Weil divisors on X. If X is non degenerate (i.e., not equivariantly isomorphic to the product of a toric variety and a torus of positive dimension), then the natural homomorphisms C l D i v C ( X ) H 2 ( X ) and C l D i v W ( X ) H 2 n - 2 c l d ( X ) are...

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