Affiliation:
1. Università di Pavia Pavia , Italy
Abstract
Abstract
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.
Reference23 articles.
1. [1] Alexeev, V., Weighted Grassmannians and stable hyperplane arrangements arXiv:0806.0881, 2008
2. [2] Alexeev, V., Moduli of weighted hyperplane arrangements, Edited by Gilberto Bini, Marti Lahoz, Emanuele Macri and Paolo Stellari. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer, Basel, 2015.
3. [3] Ascher, K., Devleming, K., Liu, Y., Wall crossing for K-moduli spaces of plane curves arXiv:1909.04576 [math.AG]
4. [4] Codogni, G., Patakfalvi, Z., Positivity of the CM line bundle for families of K-stable klt Fanos, Invent. math. 223, 811–894 (2021). https://doi.org/10.1007/s00222-020-00999-y
5. [5] De Borbon, M., Spotti, C., Local models for conical Kähler-Einstein metrics, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 147, Number 3, March 2019, Pages 1217–1230 https://doi.org/10.1090/proc/14302