Donaldson-Thomas theory for categories of homological dimension one with potential

Autor:	Davison, Ben, Meinhardt, Sven
Rok vydání:	2015
Předmět:	Mathematics - Algebraic Geometry Mathematics - Category Theory Mathematics - Representation Theory 14N35 14D23 16G20 32S60 55N33
Druh dokumentu:	Working Paper
Popis:	The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In particular, we provide rigorous proofs of all standard results concerning the integration map, wall-crossing, PT-DT correspondence, etc. following Kontsevich and Soibelman. We also show the equivalence of their approach and the one given by Joyce and Song. Secondly, we relate Donaldson-Thomas functions for such a category with arbitrary potential to those with zero potential under some mild conditions. As a result of this, we obtain a geometric interpretation of Donaldson-Thomas functions in all known realizations, i.e. mixed Hodge modules, perverse sheaves and constructible functions. Comment: 80 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.08898 Zobrazit plný text záznamu View this record from Arxiv