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RELATIONS IN THE TAUTOLOGICAL RING BY LOCALIZATION

Sato, Fumitoshi

  • Published : 2006.07.01

Abstract

We give a way to obtain formulas for ${\pi}*{\psi}^{\kappa}_{n+1}$ in terms ${\psi}$ and ${\lambda}-classes$ where ${\pi}=\bar M_{g,n+1}{\rightarrow}\bar M_{g,n}(g=0,\;1,\;2)$ by the localization theorem. By using the formulas, we obtain Kontsevich-Manin type reconstruction theorems for $\bar M_{0,\;n}(\mathbb{R^m}),\;\bar M_{1,\;n},\;and\;\bar M_{2,\;n}$. We also (re)produce a lot of well-known relations in tautological rings, such as WDVV equation, the Mumford relations, the string and dilaton equations (g = 0, 1, 2) etc. and new formulas for ${\pi}*({\lambda}_g{\psi}^{\kappa}_{n+1}+...+{\psi}^{g+{\kappa}_{n+1}$

Keywords

Gromov-Witten invariant;localization theorem

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