Monodromy at infinity of A-hypergeometric functions and toric compactifications

Mathematische Annalen

Volumn 348, Issue 4, 2010, Pages 815-831

  Takeuchi, Kiyoshi ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956965039     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-010-0501-y     Document Type: Article

References (25)

1. Adolphson A.: Hypergeometric functions and rings generated by monomials. Duke Math. J. 73, 269-290 (1994).
2. Borisov L., Horja P.: Mellin-Barnes integrals as Fourier-Mukai transforms. Adv. Math. 207, 876-927 (2006).
3. Dimca A.: Sheaves in Topology, Universitext. Springer, Berlin (2004).
4. Fulton W.: Introduction to Toric Varieties. Princeton University Press, New Jersey (1993).
5. Gelfand I.-M., Kapranov M.-M., Zelevinsky A.-V.: Hypergeometric functions and toral manifolds. Funct. Anal. Appl. 23, 94-106 (1989).
6. Gelfand I.-M., Kapranov M.-M., Zelevinsky A.-V.: Generalized Euler integrals and A-hypergeometric functions. Adv. Math. 84, 255-271 (1990).
7. Gelfand I.-M., Kapranov M.-M., Zelevinsky A.-V.: Discriminants, Resultants and Multidimensional Determinants. Birkhäuser, Boston (1994).
8. Horja, P.: Hypergeometric functions and mirror symmetry in toric varieties, arxiv: math/9912109v3.
9. Hotta R., Takeuchi K., Tanisaki T.: D-modules, Perverse Sheaves, and Representation Theory. Birkhäuser, Boston (2008).
10. Kashiwara M., Schapira P.: Sheaves on Manifolds. Springer, Berlin (1990).
11. Khovanskii A.-G.: Newton polyhedra and toroidal varieties. Funct. Anal. Appl. 11, 289-296 (1978).
12. Kouchnirenko A.-G.: Polyédres de Newton et nombres de Milnor. Invent. Math. 32, 1-31 (1976).
13. Libgober A., Sperber S.: On the zeta function of monodromy of a polynomial map. Compositio Math. 95, 287-307 (1995).
14. Massey D.: Hypercohomology of Milnor fibers. Topology 35, 969-1003 (1996).
15. Matsui, Y., Takeuchi, K.: A geometric degree formula for A-discriminants and Euler obstructions of toric varieties, arxiv: 0807. 3163v3.
16. Matsui, Y., Takeuchi, K.: Milnor fibers over singular toric varieties and nearby cycle sheaves, arxiv: 0809. 3148v2.
17. Matsui, Y., Takeuchi, K.: Monodromy at infinity, Newton polyhedra and constructible sheaves. Mathematische Zeitschrift (to appear).
18. Milnor J.: Singular Points of Complex Hypersurfaces. Princeton University Press, New Jersey (1968).
19. Oda T.: Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties. Springer, Berlin (1988).
20. Saito M., Sturmfels B., Takayama N.: Gröbner Deformations of Hypergeometric Differential Equations. Springer, Berlin (2000).
21. Schulze M., Walther U.: Irregularity of hypergeometric systems via slopes along coordinate subspaces. Duke Math. Journal 142, 465-509 (2008).
22. Schürmann J.: Topology of Singular Spaces and Constructible Sheaves. Birkhäuser, Boston (2003).
23. Takeuchi K.: Perverse sheaves and Milnor fibers over singular varieties. Adv. Stud. Pure Math. 46, 211-222 (2007).
24. Varchenko A.-N.: Zeta-function of monodromy and Newton's diagram. Invent. Math. 37, 253-262 (1976).
25. Walther U.: Duality and monodromy reducibility of A-hypergeometric systems. Math. Ann. 338, 55-74 (2007).