On the better behaved version of the GKZ hypergeometric system

Borisov, Lev A.; Paul Horja, R.

doi:10.1007/s00208-013-0913-6

On the better behaved version of the GKZ hypergeometric system

Nov, 2010

19 pages

Published in:

Math.Ann. 357 (2013) 2, 585-603,
Mathematische Annalen 357 (2013) 2, 585-603

Published: Oct 1, 2013

e-Print:

1011.5720 [math.AG]

DOI:

10.1007/s00208-013-0913-6

View in:

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Abstract: (Springer)

We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated abelian group. In contrast to the usual GKZ hypergeometric system, the rank of the better behaved GKZ hypergeometric system is always the expected one. We give largely self-contained proofs of many properties of this system. The discussion is intimately related to the study of the variations of Hodge structures of hypersurfaces in algebraic tori.

Note:

LaTex, 22 pages; v2 is a major revision: the introduction, sections 4 and 5 have been changed; section 5 is new; v3 published version

Abelian Group
Toric Variety
Hodge Structure
Finite Abelian Group
Semigroup Ring

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Figures(0)

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