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Moduli of weighted stable elliptic surfaces and invariance of log plurigenera
Author(s) -
Ascher Kenneth,
Bejleri Dori
Publication year - 2021
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12387
Subject(s) - mathematics , moduli space , moduli , elliptic curve , morphism , section (typography) , pure mathematics , boundary (topology) , domain (mathematical analysis) , surface (topology) , mathematical analysis , geometry , physics , quantum mechanics , advertising , business
Abstract Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing weighted stable elliptic surfaces — elliptic fibrations with section and marked fibers each weighted between zero and one. Moreover, we show that the domain of weights admits a wall and chamber structure, describe the induced wall‐crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical result is a proof of invariance of log plurigenera for slc elliptic surface pairs with arbitrary weights.