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Pré-Publication, Document De Travail Année : 2016

A short proof of Tian's formula for logarithmic Weil-Petersson metric

Hassan Jolany
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Résumé

In this short note, we give a short proof of Tian's formula[10] for Käh-ler potential of logarithmic Weil-Petersson metric on moduli space of log Calabi-Yau varieties (if exists!) of conic and Poincare singularities. Moreover we give a relation between logarithmic Weil-Petersson metric and the logarithmic version of Vafa-Yau semi Ricci flat metric on the family of log Calabi-Yau pairs with conical singularities. In final we consider the semi-positivity of singular logarithmic Weil-Petersson metric on the moduli space of log-Calabi-Yau varieties.
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Dates et versions

hal-01413746 , version 1 (10-12-2016)
hal-01413746 , version 2 (20-01-2017)
hal-01413746 , version 3 (14-02-2017)
hal-01413746 , version 4 (20-06-2017)

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  • HAL Id : hal-01413746 , version 1

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Hassan Jolany. A short proof of Tian's formula for logarithmic Weil-Petersson metric. 2016. ⟨hal-01413746v1⟩
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