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

Abstract

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.

arXiv comment36pages

References in corpus (8)

• Curve counting via stable pairs in the derived category
• Stable pairs and BPS invariants
• Dirichlet branes, homological mirror symmetry, and stability
• Donaldson-Thomas invariants via microlocal geometry
• The 3-fold vertex via stable pairs
• Perverse coherent sheaves (after Deligne)
• Stability conditions and Stokes factors
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds

Cited by in corpus (10)

• Chamber Structure and Wallcrossing in The ADHM Theory of Curves I
• Geometric engineering of (framed) BPS states
• Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions
• Hilbert schemes and stable pairs: GIT and derived category wall crossings
• Cobordism invariants of the moduli space of stable pairs
• Curve counting theories via stable objects I. DT/PT correspondence
• Descendents on local curves: Stationary theory
• Donaldson-Thomas invariants of certain Calabi-Yau 3-folds
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Descendent theory for stable pairs on toric 3-folds