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Intersections of tautological classes on blowups of moduli spaces of genus-1 curves. (English) Zbl 1177.14057

The moduli spaces of genus one curves with marked points and their blow-ups are considered. Naturally defined cohomology classes, the \(\psi\) classes, are studied. For the intersection numbers of these classes three recursion relations are given. Two of these recursion relations generalize the genus one string and dilation relations. The results obtained are used in other papers of the author [The reduced genus-one Gromov-Witten invariants of Calabi-Yau hypersurfaces, preprint arXiv:math/0705.2397; Geom. Topol. 12, No. 2, 1203–1241 (2008; Zbl 1167.14009)] to compute the genus one GW invariants of projective Calabi-Yau hypersurfaces.

MSC:

14H10 Families, moduli of curves (algebraic)
14D20 Algebraic moduli problems, moduli of vector bundles
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds

Citations:

Zbl 1167.14009
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