On stringy cohomology spaces

Borisov, Lev A.

doi:10.1215/00127094-2649643

On stringy cohomology spaces

Lev A. Borisov
(
- Rutgers U., Piscataway
)

May, 2012

22 pages

Published in:

Duke Math.J. 163 (2014) 6, 1105-1126

Published: Apr 15, 2014

e-Print:

1205.5463 [math.AG]

DOI:

10.1215/00127094-2649643

View in:

pdf

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Abstract: (Duke University Press)

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 our previous coauthored work with Mavlyutov, but they admit natural flat connections with respect to the appropriate parameters. This solves a longstanding question of relating the Gelfand–Kapranov–Zelevinsky (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 our coauthored work with Mavlyutov, and we prove a statement on intersection cohomology of dual cones that may be of independent interest.

Note:

21 pages, LaTeX

algebra: vertex
cohomology
duality
symmetry: mirror

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Figures(0)

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