Sheaf stable pairs on projective surfaces and birational geometry
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.
Cite
@article{arxiv.2601.00153,
title = {Sheaf stable pairs on projective surfaces and birational geometry},
author = {Caucher Birkar and Jia Jia and Artan Sheshmani and Chengxi Wang},
journal= {arXiv preprint arXiv:2601.00153},
year = {2026}
}
Comments
34 pages, comments are very welcome