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 $\small{{\pi}=\bar M_{g,n+1}{\rightarrow}\bar M_{g,n}(g=0,\;1,\;2)}$ by the localization theorem. By using the formulas, we obtain Kontsevich-Manin type reconstruction theorems for $\small{\bar M_{0,\;n}(\mathbb{R^m}),\;\bar M_{1,\;n},\;and\;\bar M_{2,\;n}}$. 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 $\small{{\pi}*({\lambda}_g{\psi}^{\kappa}_{n+1}+...+{\psi}^{g+{\kappa}_{n+1}}$
Keywords
Gromov-Witten invariant;localization theorem;
Language
English
Cited by
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