Donaldson-Thomas invariants via L_\infty-algebras
Yunfeng Jiang, University of Utah
Abstract: Let X be a smooth Calabi-Yau threefold, the Donaldson-Thomas invariants are virtual count of ideal sheaves. To every point in the Donaldson-Thomas moduli
space, we associate a cyclic dg Lie algebra L which we call Donaldson-Thomas dg Lie algebra. By transfer theorem there exists a L_\infty-algebra structure on the
cohomology H(L), from which we can write down a potential function W.
In some cses, the potential function W is holomorphic such that locally the Donaldson-thomas moduli space is the critical locus of the function
W. The pointed Donaldson-Thomas invariant is the Milnor number of the holomorphic function W.