Relations in the tautological ring by localization
Commun. Korean Math. Soc. 2006 Vol. 21, No. 3, 475-490
Printed September 1, 2006
Fumitoshi Sato
Korea Institute for Advanced Study
Abstract : We give a way to obtain formulas for $\pi_{*} \psi^k_{n+1} $ in terms of $\psi$ and $\lambda$-classes where $ \pi :\moduli{g}{n+1} \rightarrow \moduli{g}{n} (g=0,1,2)$ by the localization theorem. By using the formulas, we obtain Kontsevich--Manin type reconstruction theorems for $\moduli{0}{n}(\CP^m), \moduli{1}{n},$ and $ \moduli{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 $\pi_*(\lambda_g \psi_{n+1}^k+ \cdots + \psi_{n+1}^{g+k})$.
Keywords : Gromov-Witten invariant, localization theorem
MSC numbers : 14N10, 14N35
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd