The orbifold chow ring of toric deligne-mumford stacks

Journal of the American Mathematical Society

Volumn 18, Issue 1, 2005, Pages 193-215

  Borisov, Lev A ^a   Chen, Linda ^b,c   Smith, Gregory G ^d,e  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b Columbia University ^*  (United States)

^c OHIO STATE UNIVERSITY   (United States)

^d Program on US Russia Relations at Columbia s Harriman Institute   (United States)

^e QUEEN S UNIVERSITY   (Canada)

Author keywords

Chow ring; Crepant resolution; Deligne Mumford stack; Toric variety

Indexed keywords

EID: 13544263515     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-04-00471-0     Document Type: Article

References (29)

1. D. Abramovich, A. Corti, and A. Vistoli, Twisted bundles and admissible covers, Comm. Algebra 31 (2003), 3547-3618. MR2007376
2. D. Abramovich, T. Graber, and A. Vistoli, "Algebraic orbifold quantum products" in Orbifolds in mathematics and physics, pp. 1-24, Contemp. Math. 310, Amer. Math. Soc., Providence, RI, 2002. MR1950940 (2004c:14104)
3. V. V. Batyrev, Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs, J. Eur. Math.Soc. 1 (1999), 5-33. MR1677693 (2001j:14018)
4. L. A. Borisov, String cohomology of a toroidal singularity, J. Algebraic Geom. 9 (2000), 289-300. MR1735773 (2001b:14079)
5. W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Math. 39, Cambridge University Press, Cambridge, 1993. MR1251956 (95h:13020)
6. D. A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), 17-50. MR1299003 (95i:14046)
7. W. Chen and Y. Ruan, A New Cohomology Theory for Orbifold, arXiv:math.AG/0004129.
8. W. Chen and Y. Ruan, "Orbifold Gromov-Witten theory" in Orbifolds in mathematics and physics, pp. 25-85, Contemp. Math. 310, Amer. Math. Soc., Providence, RI, 2002. MR1950941 (2004k:53145)
9. P. Deligne and M. Rapoport, "Les schémas de modules de courbes elliptiques" in Modular functions of one variable, II, pp. 143-316, Lecture Notes in Math. 349, Springer, Berlin, 1973. MR0337993 (49:2762)
10. D. Edidin, "Notes on the construction of the moduli space of curves" in Recent progress in intersection theory, pp. 85-113, Trends Math., Birkhäuser Boston, Boston, MA, 2000. MR1849292 (2002f:14039)
11. D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer-Verlag, New York, 1995. MR1322960 (97a:13001)
12. D. Eisenbud and J. Harris, The geometry of schemes, Graduate Texts in Math. 197, Springer-Verlag, New York, 2000. MR1730819 (2001d:14002)
13. D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J. 84 (1996), 1-45. MR1394747 (97d:13031)
14. B. Fantechi and L. Göttsche, Orbifold cohomology for global quotients, Duke Math. J. 117 (2003), 197-227. MR1971293 (2004h:14062)
15. W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, Princeton University Press, Princeton, NJ, 1993. MR1234037 (94g:14028)
16. Y. Jiang, The Chen-Ruan cohomology of weighted projective spaces, arXiv:math.AG/0304140.
17. J. Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 32, Springer-Verlag, Berlin, 1996. MR1440180 (98c:14001)
18. T, Invent. Math. 136 (1999), 233-271. MR1681089 (2000i:14071)
19. G. Laumon and L. Moret-Bailly, Champs algébriques, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 39, Springer-Verlag, Berlin, 2000. MR1771927 (2001f:14006)
20. I. Moerdijk, "Orbifolds as groupoids: an introduction" in Orbifolds in mathematics and physics, pp. 205-222, Contemp. Math. 310, Amer. Math. Soc., Providence, RI, 2002. MR1950948 (2004c:22003)
21. T. Oda, Convex bodies and algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 15, Springer-Verlag, Berlin, 1988. MR0922894 (88m:14038)
22. M. Poddar, "Orbifold cohomology group of toric varieties" in Orbifolds in mathematics and physics, pp. 223-231, Contemp. Math. 310, Amer. Math. Soc., Providence, RI, 2002. MR1950949 (2003j:14068)
23. Y. Ruan, Cohomology Ring of Crepant Resolutions of Orbifolds, arXiv:math.AG/0108195.
24. R. Stanley, "Generalized H-vectors, intersection cohomology of toric varieties, and related results" in Commutative algebra and combinatorics, pp. 187-213, Adv. Stud. Pure Math. 11, North-Holland, Amsterdam, 1987. MR0951205 (89f:52016)
25. B. Uribe, Orbifold cohomology of the symmetric product, Comm. Anal. Geom. (to appear), arXiv:math.AT/0109125.
26. A. Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989), 613-670. MR1005008 (90k:14004)
27. C. A. Weibel, An introduction to homological algebra. Cambridge Studies in Advanced Math. 38, Cambridge University Press, Cambridge, 1994. MR1269324 (95f:18001)
28. T. Yasuda, Twisted jets, motivic measure and orbifold cohomology, Compos. Math. 140 (2004), 396-422. MR2027195
29. G. M. Ziegler, Lectures on polytopes, Graduate Texts in Math. 152, Springer-Verlag, New York, 1995. MR1311028 (96a:52011)