# zbMATH — the first resource for mathematics

$$A$$-hypergeometric systems and relative cohomology. (English) Zbl 07301549
##### MSC:
 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Full Text:
##### References:
 [1] Adolphson, A., Hypergeometric functions and rings generated by monomials, Duke Math. J.73(2) (1994) 269-290. · Zbl 0804.33013 [2] Adolphson, A. and Sperber, S., Dwork cohomology, de Rham cohomology, and hypergeometric functions, Amer. J. Math.122(2) (2000) 319-348. · Zbl 0980.14017 [3] Aspinwall, P. S., Greene, B. R. and Morrison, D. R., The monomial-divisor mirror map, Internat. Math. Res. Not.12 (1993) 319-337. · Zbl 0798.14030 [4] Baldassarri, F. and D’Agnolo, A., On Dwork cohomology and algebraic $$D$$-modules, in Geometric Aspects of Dwork Theory (2003), pp. 245-253. [5] Dimca, A., Maaref, F., Sabbah, C. and Saito, M., Dwork cohomology and algebraic $$\mathcal{\mathcal{D}}$$-module, Math. Ann.318(1) (2000) 107-125. · Zbl 0985.14007 [6] Gel’fand, I. M., Zelevinskii, A. V. and Kapranov, M. M., Hypergeometric functions and toral manifolds, Funktsional. Anal. i Prilozhen.23(2) (1989) 94-106. [7] Hosono, S., Lian, B. and Yau, S.-T., Maximal degeneracy points of GKZ systems, J. Amer. Math. Soc.10(2) (1997) 427-443. · Zbl 0874.32007 [8] Huang, A., Lian, B., Yau, S.-T. and Zhu, X., Chain integral solutions to tautological systems, Math. Res. Lett.23 (2016) 1721-1736. · Zbl 1364.14031 [9] Huang, A., Lian, B. and Zhu, X., Period integrals and the Riemann-Hilbert correspondence, J. Differential Geometry104 (2016) 325-369. · Zbl 1387.14042 [10] Katz, N. M., On the differential equations satisfied by period matrices, 35Inst. Hautes Études Sci. Publ. Math. (1968) 223-258. [11] Reichelt, T., Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules, Compositio Math.150 (2014) 911-941. · Zbl 1315.14016 [12] Schulze, M. and Walther, U., Hypergeometric $$D$$-modules and twisted Gauss-Manin systems, J. Algebra322(9) (2009) 3392-3409. · Zbl 1181.13023 [13] Zhou, J., GKZ hypergeometric series for the Hesse pencil, chain integrals and orbifold singularities, SIGMA13(30) 30. · Zbl 1453.14106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.