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Relations in the tautological ring by localization

Fumitoshi Sato
대한수학회 (The Korean Mathematical Society)|2006.07|대한수학회논문집 (Communications of the KMS)|제21권 제3호|pp. 475-490

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주제분류수학

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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 thelocalization theorem. By using the formulas, we obtainKontsevich--Manin type reconstruction theorems formoduli{0}{n}(CP^m), moduli{1}{n}, and moduli{2}{n}. Wealso (re)produce a lot of well-known relations in tautologicalrings, such as WDVV equation, the Mumford relations, the stringand dilaton equations (g=0,1,2) etc. and new formulas forpi_*(lambda_g psi_{n+1}^k+ cdots + psi_{n+1}^{g+k}).

참고문헌 (16)

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