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Register a new userOn the large genus asymptotics of Weil-Petersson volumes
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Authors
Peter Zograf
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A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of the Weil-Petersson volumes is computed. Asymptotic formulas for the intersection numbers involving $psi$-classes are conjectured as well. The accuracy of the formulas is high enough to believe that they are exact.
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In this work we show that the Weil-Petersson volume (which coincides with the CM degree) in the case of weighted points in the projective line is continuous when approaching the Calabi-Yau geometry from the Fano geometry. More specifically, the CM volume computed via localization converges to the geometric volume, computed by McMullen with different techniques, when the sum of the weights approaches the Calabi-Yau geometry.
Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory of Weil-Petersson geometry on the stringy Kahler moduli space. A few basic examples are studied. In particular, we identify our Weil-Petersson metric with the Bergman metric on a Siegel modular variety in the case of the self-product of an elliptic curve.
We study the Weil-Petersson geometry for holomorphic families of Riemann Surfaces equipped with the unique conical metric of constant curvature -1.
Recently Bonisch-Fischbach-Klemm-Nega-Safari discovered, via numerical computation, that the leading asymptotics of the l-loop Banana Feynman amplitude at the large complex structure limit can be described by the Gamma class of a degree (1,...,1) Fano hypersurface F in (P^1)^{l+1}. We confirm this observation by using a Gamma-conjecture type result for F.
We show that the flow on a Bers slice given by the Weil-Petersson gradient vector field of renormalized volume is globally attracting to its fuchsian basepoint.
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