Gravitational Descendants and the Moduli Space of Higher Spin Curves

Details Gravitational Descendants and the Moduli Space of Higher Spin Curves Gravitational Descendants and the Moduli Space of Higher Spin Curves

2000-09-06

arxiv.org/abs/math/0009066v2

Mathematics

Algebraic Geometry

12 pages, minor changes

Scientific paper

The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of $r$-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a priori analog in the theory of Gromov-Witten invariants), in terms of the multiplicativity of the virtual class. We prove that the Descent Axiom holds in the convex case, and consequently in genus zero.

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