Toric complete intersections and weighted projective space

Journal of Geometry and Physics

Volumn 46, Issue 2, 2003, Pages 159-173

  Kreuzer, Maximilian ^a   Riegler, Erwin ^a   Sahakyan, David A ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Calabi Yau manifolds; Mirror symmetry; Newton polyhedra; String and superstring theories; Toric varieties

Indexed keywords

EID: 0037401051     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(02)00124-9     Document Type: Article

References (42)

1. P. Green, T. Hübsch, Calabi-Yau manifolds as complete intersections in products of complex projective spaces, Commun. Math. Phys. 109 (1987) 99.
2. P. Candelas, A.M. Dale, C.A. Lutken, R. Schimmrigk, Complete intersection Calabi-Yau manifolds, Nucl. Phys B. 298 (1988) 493.
3. W. Lerche, C. Vafa, N. Warner, Chiral rings in N = 2 superconformal theories, Nucl. Phys. B 324 (1989) 427.
4. 4 , Nucl. Phys. B 341 (1990) 383.
5. M. Kreuzer, H. Skarke, No mirror symmetry in Landau-Ginzburg spectra! Nucl. Phys. B 388 (1992) 113. hep-th/9205004.
6. A. Klemm, R. Schimmrigk, Landau-Ginzburg string vacua, Nucl. Phys. B 411 (1994) 559. hep-th/9204060.
7. V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493. alg-geom/9310003.
8. M. Kreuzer, H. Skarke, Classification of reflexive polyhedra in three dimensions, Adv. Theor. Math. Phys. 2 (1998) 847. hep-th/9805190.
9. M. Kreuzer, H. Skarke, Complete classification of reflexive polyhedra in four dimensions. hep-th/0002240.
10. M. Kreuzer, H. Skarke, On the classification of reflexive polyhedra, Commun. Math. Phys. 185 (1997) 495. hep-th/9512204.
11. M. Kreuzer, H. Skarke, Reflexive polyhedra, weights and toric Calabi-Yau fibrations. math.AG/0001106.
12. A. Klemm, unpublished.
13. A. Klemm, S. Theisen, Mirror maps and instanton sums for complete intersections in weighted projective space, Mod. Phys. Lett. A 9 (1994) 1807. hep-th/9304034.
14. V.V. Batyrev, L.A. Borisov, Dual cones and mirror symmetry for generalized Calabi-Yau manifolds, in: S.-T. Yau (Ed.), Mirror Symmetry II. alg-geom/9402002.
15. V.V. Batyrev, L.A. Borisov, On Calabi-Yau complete intersections in toric varieties, in: Proceedings of the Trento Conference, 1994. alg-geom/9412017.
16. V.V. Batyrev, L.A. Borisov, Mirror duality and string theoretic Hodge numbers. alg-geom/9509009.
17. A.R. Fletcher, Working with complete intersections, Bonn preprint MPI/89-35, 1989.
18. M. Kreuzer, H. Skarke, On the classification of quasihomogeneous functions, Commun. Math. Phys. 150 (1992) 137. hep-th/9202039.
19. H. Skarke, Weight systems for toric Calabi-Yau varieties and reflexivity of Newton polyhedra, Mod. Phys. Lett. A 11 (1996) 1637. alg-geom/9603007.
20. A. Klemm, B. Lian, S.-S. Roan, S.-T. Yau, Calabi-Yau fourfolds for M- and F-theory compactifications, Nucl. Phys. B 518 (1998) 515. hep-th/9701023.
21. M. Kreuzer, H. Skarke, Calabi-Yau fourfolds and toric fibrations, J. Geom. Phys. 466 (1997) 1. hep-th/9701175.
22. D. Cox, The homogeneous coordinate ring of a toric variety, J. Alg. Geom. 4 (1995) 17. alg-geom/9210008.
23. L.A. Borisov, Towards the mirror symmetry for Calabi-Yau complete intersections in Gorenstein toric Fano varieties. alg-geom/9310001.
24. M. Kreuzer, H. Skarke. http://hep.itp.tuwien.ac.at/~kreuzer/CY.html.
25. W. Fulton, Introduction to Toric Varieties, Princeton University Press, Princeton, NJ, 1993.
26. T. Oda, Convex Bodies and Algebraic Geometry, Springer, Berlin, 1988.
27. D. Cox, Recent developments in toric geometry. alg-geom/9606016.
28. M. Kreuzer, Strings on Calabi-Yau Spaces and Toric Geometry, hep-th/0103243.
29. M. Kreuzer, H. Skarke, All Abelian symmetries of Landau-Ginzburg potentials, Nucl. Phys. B 405 (1993) 305. hep-th/9211047.
30. M. Kreuzer, H. Skarke, Landau-Ginzburg orbifolds with discrete torsion, Mod. Phys. Lett. A 10 (1995) 1073. hep-th/9412033.
31. P. Berglund, T. Hübsch, A generalized construction of mirror manifolds, Nucl. Phys. B 393 (1993) 377. hep-th/9201014.
32. M. Kreuzer, The mirror map for invertible LG models, Phys. Lett. B 328 (1994) 312. hep-th/9402114;
33. M. Kreuzer, H. Skarke, Orbifolds with discrete torsion and mirror symmetrie, Phys. Lett. B 357 (1995). hep-th/9505120.
34. M. Kreuzer,H. Skarke, ADE string vacua with discrete torsion, Phys. Lett.B318 (1993) 305. hep-th/9307145.
35. P.S. Aspinwall, J. Louis, On the ubiquity of K3 fibrations in string duality, Phys. Lett. B 369 (1996) 233. hep-th/9510234.
36. C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403. hep-th/9602022.
37. P.S. Aspinwall, K3 surfaces and string duality. hep-th/9611137.
38. P. Candelas, A. Font, Duality between the webs of heterotic and type II vacua, Nucl. Phys. B 511 (1998) 295. hep-th/9603170.
39. A. Avram, M. Kreuzer, M. Mandelberg, H. Skarke, Searching for K3 fibrations, Nucl. Phys. B 494 (1997) 567. hep-th/9610154.
40. R. Stanley, Generalized H-vectors, intersection cohomology of toric varieties, and related results, Adv. Stud. Pure Math. 11 (1987) 187-213.
41. V.I. Danilov, A.G. Khovanskii, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers, Math. USSR Izvestiya 29 (1987) 279-298.
42. M. Kreuzer, H. Skarke, PALP: A package analyzing lattice polyhedra with applications to toric geometry, (2002). math.SC/0204356.