Title :

Canonical metric on moduli spaces of log Calabi-Yau varieties

Author(s) :

Jolany, Hassan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Moduli Spaces
Kahler-Ricci flow
Singularites
Kahler-Einstein metrics
Calabi-Yau manifolds
Weil-Petersson metric

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this paper, we give a short proof of closed formula [9],[18] of logarithmic Weil-Peterssonmetric on moduli space of log Calabi-Yau varieties (if exists!) of conicand Poincare singularities and its connection with ...
Show more >In this paper, we give a short proof of closed formula [9],[18] of logarithmic Weil-Peterssonmetric on moduli space of log Calabi-Yau varieties (if exists!) of conicand Poincare singularities and its connection with Bismut-Vergne localization formula.Moreover we give a relation between logarithmic Weil-Petersson metric andthe logarithmic version of semi Ricci flat metric on the family of log Calabi-Yaupairs with conical singularities. We highlight Bismut-Gillet-Soule fiberwise integralformula for logarithmic Weil-Petersson metric on moduli space of polarizedlog Calabi-Yau spaces by using fiberwise Ricci flat metric. In final we considerthe semi-positivity of singular logarithmic Weil-Petersson metric on the modulispace of log-Calabi-Yau varieties. Moreover, we show that Song-Tian-Tsuji measureis bounded along Iitaka fibration if and only if central fiber has log terminalsingularities and we consider the goodness of fiberwise Calabi-Yau metric in thesense of Mumford and goodness of singular Hermitian metric corresponding toSong-Tian-Tsuji measure. We also mention that the Song-Tian-Tsuji measure isbounded near origin if and only if after a finite base change the Calabi-Yau familyis birational to one with central fiber a Calabi-Yau variety with at worst canonicalsingularities.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL