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arXiv · 1205.5463

On stringy cohomology spaces

Lev A. Borisov
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Abstract

We modify the definition of the families of $A$ and $B$ stringy cohomology spaces associated to a pair of dual reflexive Gorenstein cones. The new spaces have the same dimension as the ones defined in the joint paper with Mavlyutov \cite{BM}, but they admit natural flat connections with respect to the appropriate parameters. This solves a longstanding question of relating GKZ hypergeometric system to stringy cohomology. We construct products on these spaces by vertex algebra techniques. In the process, we fix a minor gap in \cite{BM} and prove a statement on intersection cohomology of dual cones that may be of independent interest.

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Lev A. Borisov. 2013-09-07. On stringy cohomology spaces. https://doi.org/10.1215/00127094-2649643

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