Invariance of tautological equations II: Gromov-Witten theory
By Y.-P. Lee. 2006
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where C? are connected components of C, C Uf=1C{. By the definition given in [16], the curves in the image of t/ have at most one more connected component. Therefore, the connected components of the image curves would have either smaller genus or the same genus but less marked points than those of the domain curves. It is therefore easy to see that these operators give an algorithm in producing tautological relations inductively. This was explained in Part I. In Part II, the focus moves to Gromov-Witten theory. One of the main themes of the current work is to study the interplay between Gromov-Witten theory and the moduli of curves. The idea of studying and utilizing this interaction is not new. One such example is given by the localization technique in Gromov-Witten theory. The fixed point loci on moduli of stable maps to projective spaces are moduli of curves (or more precisely their quotients by finite groups). Therefore, the known results on moduli of curves can be used to calculate Gromov-Witten invariants.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e058b24a5b33b3af471a1aea708ba431d1051423
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