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

Sergey Mozgovoy; Markus Reineke

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arXiv · 1310.4991

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

Sergey Mozgovoy·Markus Reineke

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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 by Weng for the ranks 2 and 3, and we prove the counting miracle conjecture.

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BibTeX RIS

Sergey Mozgovoy, Markus Reineke. 2013-10-18. Moduli spaces of stable pairs and non-abelian zeta functions of curves via wall-crossing. https://arxiv.org/abs/1310.4991

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