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Toric residue mirror conjecture for Calabi-Yau complete intersections
Author(s):
Kalle
Karu
Journal:
J. Algebraic Geom.
14
(2005),
741-760.
Posted:
April 27, 2005
MathSciNet review:
2147350
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
We prove two conjectures of V. Batyrev and E. Materov. The first one is the toric residue mirror conjecture for Calabi-Yau complete intersections in Gorenstein toric Fano varieties. The second conjecture relates the homogeneous parts of the toric residue to the mixed volumes of polytopes.
References:
-
- 1.
- G. Barthel, J.-P. Brasselet, K.-H. Fieseler, L. Kaup, Equivariant intersection cohomology of toric varieties, Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), 45-68, Contemp. Math., 241, Amer. Math. Soc., Providence, RI, 1999. MR 1718136 (2001i:14030)
- 2.
- V. V. Batyrev, E. N. Materov, Toric Residues and Mirror Symmetry, Dedicated to Yuri I. Manin on the occasion of his 65th birthday. Mosc. Math. J. 2 (2002), no. 3, 435-475. MR 1988969 (2005a:14070)
- 3.
- V. V. Batyrev, E. N. Materov, Mixed toric residues and Calabi-Yau complete intersections, Calabi-Yau varieties and mirror symmetry (Toronto, ON, 2001), 3-26, Fields Inst. Commun., 38, Amer. Math. Soc., Providence, RI, 2003. MR 2019144 (2005b:14088)
- 4.
- L. A. Borisov, Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties, preprint math.AG/9310001.
- 5.
- L. A. Borisov, Higher Stanley-Reisner rings and toric residues, Compos. Math. 141 (2005), no. 1, 161-174. MR 2099774
- 6.
- M. Brion, The structure of the polytope algebra, Tohoku Math. J. (2) 49 (1997), no. 1, 1-32. MR 1431267 (98a:52019)
- 7.
- M. Brion, M. Vergne, Arrangement of hyperplanes. I. Rational functions and Jeffrey-Kirwan residue, Ann. Sci. Ãcole Norm. Sup. (4) 32 (1999), no. 5, 715-741. MR 1710758 (2001e:32039)
- 8.
- E. Cattani, A. Dickenstein, B. Sturmfels, Residues and resultants, J. Math. Sci. Univ. Tokyo 5 (1998), no. 1, 119-148. MR 1617074 (2000b:14065)
- 9.
- D. Cox, Toric residues, Ark. Mat. 34 (1996), no. 1, 73-96. MR 1396624 (97e:14062)
- 10.
- A. Szenes, M. Vergne, Toric reduction and a conjecture of Batyrev and Materov, Invent. Math. 158 (2004), no. 3, 453-495. MR 2104791
Additional Information:
Kalle
Karu
Affiliation:
Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C. Canada V6T 1Z2
Email:
karu@math.ubc.ca
DOI:
10.1090/S1056-3911-05-00410-8
PII:
S 1056-3911(05)00410-8
Received by editor(s):
October 20, 2004
Posted:
April 27, 2005
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