1. Tau functions, Prym-Tyurin classes and loci of degenerate differentials
- Author
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Dmitry Korotkin, Adrien Sauvaget, Peter Zograf, Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Analyse, Géométrie et Modélisation (AGM - UMR 8088), and Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
- Subjects
14F10 ,Mathematics - Differential Geometry ,Pure mathematics ,cyclic covers ,Divisor ,General Mathematics ,Picard group ,Holomorphic function ,Algebraic geometry ,14H70 ,01 natural sciences ,Mathematics - Algebraic Geometry ,symbols.namesake ,Mathematics::Algebraic Geometry ,integrable systems ,Genus (mathematics) ,n-differentials ,0103 physical sciences ,FOS: Mathematics ,2018. 2010 Mathematics Subject Classification. 14H15 ,Ramanujan tau function ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics ,November 11 ,14C22 Moduli space of curves ,010102 general mathematics ,Zero (complex analysis) ,Bergman tau function ,16. Peace & justice ,14H15, 14F10, 14H70, 30F30, 14C22 ,30F30 ,Moduli space ,Differential Geometry (math.DG) ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,symbols ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,010307 mathematical physics - Abstract
We study the rational Picard group of the projectivized moduli space of holomorphic n-differentials on complex genus g stable curves. We define (n - 1) natural classes in this Picard group that we call Prym-Tyurin classes. We express these classes as linear combinations of boundary divisors and the divisor of n-differentials with a double zero. We give two different proofs of this result, using two alternative approaches: an analytic approach that involves the Bergman tau function and its vanishing divisor and an algebro-geometric approach that involves cohomological computations on the universal curve., 26 pages, 1 figure, comments are welcome
- Published
- 2019
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