RELATIONS IN THE TAUTOLOGICAL RING BY LOCALIZATION

Title & Authors
RELATIONS IN THE TAUTOLOGICAL RING BY LOCALIZATION
Sato, Fumitoshi;

Abstract
We give a way to obtain formulas for $\small{{\pi}*{\psi}^{\kappa}_{n+1}}$ in terms $\small{{\psi}}$ and $\small{{\lambda}-classes}$ where ${\pi} Keywords Gromov-Witten invariant;localization theorem; Language English Cited by References 1. M. Atiyah, and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28 2. K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45-88 3. A. Bertram and H. Kley, New recursions for genus-zero Gromov- Witten invariants, arXiv:math.AG/0007082 4. A. Bertram, Another Way to enumerate rational curves with Torus Actions, to appear in Invent. Math 5. A. Bertram, Using symmetry to count rational curves, Contemporary Math. vol. 312 (2002), 87-99 6. D. Edidin and W. Graham, Localization in equivariant intersection theory and the Bott residue formula, Amer. J. Math. 120 (1998), no. 3, pp. 619-636 7. C. Faber, A conjectural description of the tautological ring of the moduli space of curves, Moduli of Curves and Abelian Varieties, Aspects Math., E33, pp. 109-129 8. W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic Geometry-Santa Cruz 1995, Proc. Sympos. Pure Math., 62, Part 2, pp. 45-96 9. E. Getzler, Topological recursion relations in genus 2, Integrable Systems and Algebraic Geometry (Kobe/kyoto, 1997), pp. 73-106 10. A. Givental, Equivariant Gromou-Witten invariants, Internet. Math. Res. Notices. 1996 (1996), no. 13, 613-663 11. T. Graber and R. Vakil, On the tautological ring of$\overline{M}_{g,n}$, Turkish J. Math. 25 (2001), no. 1, 237-243 12. T. Graber and R. Pandharipande, Localization of uirtual classes, Invent. Math 135 (1999), no. 2, 487-518 13. K. Hori, Constraints for topological strings in D$\geq\$ 1, Nucl.Phys. B439 (1995), 395-423

14.
E. Katz, Topological recursion relations by localization, arXiv:math.AG/0310050

15.
J. Kock, Notes on Psi Classes, unpublished

16.
M. Kontsevich, Enumeration of rational curves via torus actions. In R. Dijkgraaf, C. Faber, and G. van der Geer, editors, The moduli space of curves, vol. 129 of Progress in Mathematics, pp.335-368

17.
D. Mumford, Towards an enumerative geometry of the moduli space of curves, Arithmetic and Geometry, 1983, vol. II, pp.272-327