Sheaf stable pairs on projective surfaces and birational geometry

Caucher Birkar; Jia Jia; Artan Sheshmani; Chengxi Wang

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arXiv · 2601.00153

Sheaf stable pairs on projective surfaces and birational geometry

Caucher Birkar·Jia Jia·Artan Sheshmani·Chengxi Wang

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Abstract

We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth projective surface. Having fixed the Chern character of E, the resulting moduli space is isomorphic to some subscheme of the Quot-scheme parametrising quotient sheaves of appropriate Chern character. We establish a connection between moduli space of higher rank stable pairs and stable minimal models induced by the sheaf E and sections s_i and the relative lc model of base surface, and use birational geometry of minimal models to analyse in detail the components of the fibre of the Hilbert-Chow morphism from the moduli space to the Hilbert scheme of effective Cartier divisors on the base surface.

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BibTeX RIS

Caucher Birkar, Jia Jia, Artan Sheshmani, Chengxi Wang. 2026-01-01. Sheaf stable pairs on projective surfaces and birational geometry. https://arxiv.org/abs/2601.00153

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