CURVE COUNTING THEORIES VIA STABLE OBJECTS I.DT/PT CORRESPONDENCE

摘要

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 se-ries 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 [25, Con-jecture 3.3], which claims the equality of the generating series of Donaldson-Thomas invariants and counting invariants of stable pairs. In a subsequent paper [28], we will apply the method used in this paper to show the transformation formula of our generating series under flops and the generalized McKay correspondence by Van den Bergh [10].