Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing

Sergey Mozgovoy[1]; Markus Reineke[2]

  • [1] School of Mathematics, Trinity College Dublin College Green, Dublin 2, Ireland
  • [2] Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Gaußstr. 20, D-42097 Wuppertal, Deutschland

Journal de l’École polytechnique — Mathématiques (2014)

  • Volume: 1, page 117-146
  • ISSN: 2270-518X

Abstract

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In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-crossing formula for the latter invariants and obtain an explicit formula for these invariants in terms of the motive of a curve. Previously, formulas for these invariants were known only for rank 2 due to Thaddeus and for rank 3 due to Muñoz. Using these results we obtain an explicit formula for the non-abelian zeta functions, we check the uniformity conjecture of Weng for the ranks 2 and 3, and we prove the counting miracle conjecture.

How to cite

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Mozgovoy, Sergey, and Reineke, Markus. "Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing." Journal de l’École polytechnique — Mathématiques 1 (2014): 117-146. <http://eudml.org/doc/275605>.

@article{Mozgovoy2014,
abstract = {In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-crossing formula for the latter invariants and obtain an explicit formula for these invariants in terms of the motive of a curve. Previously, formulas for these invariants were known only for rank 2 due to Thaddeus and for rank 3 due to Muñoz. Using these results we obtain an explicit formula for the non-abelian zeta functions, we check the uniformity conjecture of Weng for the ranks 2 and 3, and we prove the counting miracle conjecture.},
affiliation = {School of Mathematics, Trinity College Dublin College Green, Dublin 2, Ireland; Fachbereich C, Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Gaußstr. 20, D-42097 Wuppertal, Deutschland},
author = {Mozgovoy, Sergey, Reineke, Markus},
journal = {Journal de l’École polytechnique — Mathématiques},
keywords = {Stable pairs; vector bundles; wall-crossing formulas; higher zeta functions; stable pairs; vector bundles on a curve; moduli spaces; motivic invariants},
language = {eng},
pages = {117-146},
publisher = {École polytechnique},
title = {Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing},
url = {http://eudml.org/doc/275605},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Mozgovoy, Sergey
AU - Reineke, Markus
TI - Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing
JO - Journal de l’École polytechnique — Mathématiques
PY - 2014
PB - École polytechnique
VL - 1
SP - 117
EP - 146
AB - In this paper we study and relate the non-abelian zeta functions introduced by Weng and invariants of the moduli spaces of arbitrary rank stable pairs over curves. We prove a wall-crossing formula for the latter invariants and obtain an explicit formula for these invariants in terms of the motive of a curve. Previously, formulas for these invariants were known only for rank 2 due to Thaddeus and for rank 3 due to Muñoz. Using these results we obtain an explicit formula for the non-abelian zeta functions, we check the uniformity conjecture of Weng for the ranks 2 and 3, and we prove the counting miracle conjecture.
LA - eng
KW - Stable pairs; vector bundles; wall-crossing formulas; higher zeta functions; stable pairs; vector bundles on a curve; moduli spaces; motivic invariants
UR - http://eudml.org/doc/275605
ER -

References

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