Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2
Algebraic Geometry
2016-02-15 v4 High Energy Physics - Theory
Abstract
Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k=1, 2 or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinatorial formula for the invariants when k=2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of Joyce-Song in some cases.
Keywords
Cite
@article{arxiv.1309.0056,
title = {Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2},
author = {Amin Gholampour and Artan Sheshmani},
journal= {arXiv preprint arXiv:1309.0056},
year = {2016}
}
Comments
Contact updated, 22 pages, Adv. Theor. Math. Phys., Vol 19, 3, 673-699, (2015)