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- W2004878768 abstract "Let X be a Calabi-Yau 3-fold, T=D^b(coh(X)) the derived category of coherent sheaves on X, and Stab(T) the complex manifold of Bridgeland stability conditions Z on T. It is conjectured that one can define rational numbers J^a(Z) for Z in Stab(T) and a in the numerical Grothendieck group K(T) generalizing Donaldson-Thomas invariants, which `count' Z-semistable (complexes of) coherent sheaves on X in class a, and whose transformation law under change of Z is known. This paper explains how to combine such invariants J^a(Z), if they exist, into a family of holomorphic generating functions F^a:Stab(T) --> C. Surprisingly, requiring the F^a to be continuous and holomorphic determines them essentially uniquely, and implies they satisfy a p.d.e., which can be interpreted as the flatness of a connection over Stab(T) with values in an infinite-dimensional Lie algebra L. The author believes that underlying this mathematics there should be some new physics, in String Theory and Mirror Symmetry. String Theorists are invited to work out and explain this new physics." @default.
- W2004878768 created "2016-06-24" @default.
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- W2004878768 date "2007-05-10" @default.
- W2004878768 modified "2023-10-16" @default.
- W2004878768 title "Holomorphic generating functions for invariants counting coherent sheaves on Calabi–Yau 3–folds" @default.
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- W2004878768 doi "https://doi.org/10.2140/gt.2007.11.667" @default.
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