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Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula
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Yukinobu Toda
Published/Copyright:
December 22, 2011
Abstract
The goal of the present paper is to show the transformation formula of Donaldson–Thomas invariants on smooth projective Calabi–Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative Donaldson–Thomas invariants, introduced by B. Szendrői in a local (−1, −1)-curve example, to an arbitrary flopping contraction from a smooth projective Calabi–Yau 3-fold. The transformation formula between such invariants and the usual Donaldson–Thomas invariants are also established. These formulas will be deduced from the wall-crossing formula in the space of weak stability conditions on the derived category.
Received: 2010-03-01
Revised: 2011-04-07
Published Online: 2011-12-22
Published in Print: 2013-02
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula
- Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions
- n-angulated categories
- Hypertrees, projections, and moduli of stable rational curves
- Locally conformally flat quasi-Einstein manifolds
- Annihilating Selmer modules
- Fitting ideals of ℓ-adic realizations of Picard 1-motives and class groups of global function fields
