Generating functions of stable pair invariants via wall-crossings in derived categories

Details Generating functions of stable pair invariants via wall-crossings in derived categories Generating functions of stable pair invariants via wall-crossings in derived categories

2008-05-31

arxiv.org/abs/0806.0062v1

Mathematics

Algebraic Geometry

36pages

Scientific paper

The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of limit stable objects seem relevant to the rationality conjecture of the generating functions of Pandharipande-Thomas invariants. In this article, we shall make it clear how wall-crossing formula of the counting invariants of limit stable objects solves the above conjecture.

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