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

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Tau functions, Prym-Tyurin classes and loci of degenerate differentials. / Korotkin, Dmitry; Sauvaget, Adrien; Zograf, Peter.

In: Mathematische Annalen, Vol. 375, No. 1-2, 08.10.2019, p. 213-246.

Research output: Contribution to journal › Article › peer-review

Author

Korotkin, Dmitry ; Sauvaget, Adrien ; Zograf, Peter. / Tau functions, Prym-Tyurin classes and loci of degenerate differentials. In: Mathematische Annalen. 2019 ; Vol. 375, No. 1-2. pp. 213-246.

BibTeX

@article{58aa47a1865e4f8f9984414ac09e322a,

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

abstract = "We study the rational Picard group of the projectivized moduli space PM¯g(n) 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.",

keywords = "Bergman tau function, Cyclic covers, Integrable systems, Moduli space of curves, n-differentials",

author = "Dmitry Korotkin and Adrien Sauvaget and Peter Zograf",

note = "Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2019",

month = oct,

day = "8",

doi = "10.1007/s00208-019-01836-1",

language = "English",

volume = "375",

pages = "213--246",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer Nature",

number = "1-2",

}

RIS

TY - JOUR

T1 - Tau functions, Prym-Tyurin classes and loci of degenerate differentials

AU - Korotkin, Dmitry

AU - Sauvaget, Adrien

AU - Zograf, Peter

PY - 2019/10/8

Y1 - 2019/10/8

N2 - We study the rational Picard group of the projectivized moduli space PM¯g(n) 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.

AB - We study the rational Picard group of the projectivized moduli space PM¯g(n) 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.

KW - Bergman tau function

KW - Cyclic covers

KW - Integrable systems

KW - Moduli space of curves

KW - n-differentials

UR - http://www.scopus.com/inward/record.url?scp=85067235595&partnerID=8YFLogxK

U2 - 10.1007/s00208-019-01836-1

DO - 10.1007/s00208-019-01836-1

M3 - Article

AN - SCOPUS:85067235595

VL - 375

SP - 213

EP - 246

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -

ID: 98425834