Tau functions, Prym-Tyurin classes and loci of degenerate differentials

Autor: Dmitry Korotkin, Adrien Sauvaget, Peter Zograf
Přispěvatelé: Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
Rok vydání: 2019
Předmět:
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
Zdroj: Mathematische Annalen
Mathematische Annalen, Springer Verlag, 2019, 375 (1-2), pp.213-246. ⟨10.1007/s00208-019-01836-1⟩
ISSN: 1432-1807
0025-5831
DOI: 10.1007/s00208-019-01836-1
Popis: 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
Databáze: OpenAIRE
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