Curve counting theories via stable objects II: DT/ncDT/flop formula
نویسنده
چکیده
The goal of the present paper is to show the transformation formula of DonaldsonThomas invariants on smooth projective Calabi-Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative DonaldsonThomas 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 wallcrossing formula in the space of weak stability conditions on the derived category.
منابع مشابه
Curve Counting Theories via Stable Objects I. Dt/pt Correspondence
The purpose of this paper is to study curve counting on Calabi-Yau 3-folds via wall-crossing phenomena in the derived category. We will study the generating series of Donaldson-Thomas-type invariants without virtual fundamental cycles, i.e. the Euler characteristics of the relevant moduli spaces. The main result is to show the Euler characteristic version of the Pandharipande-Thomas conjecture ...
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