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Gravitational descendants and the moduli space of higher spin curves. (English) Zbl 0986.81105
Previato, Emma (ed.), Advances in algebraic geometry motivated by physics. Proceedings of the AMS special session on enumerative geometry in physics, University of Massachusetts, Lowell, MA, USA, April 1-2, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 276, 167-177 (2001).
Summary: The purpose of this note is to 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.
For the entire collection see [Zbl 0966.00024].

##### MSC:
 81T70 Quantization in field theory; cohomological methods 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 14H10 Families, moduli of curves (algebraic)
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