Non-birational twisted derived equivalences in abelian GLSMs

Communications in Mathematical Physics

Volumn 294, Issue 3, 2010, Pages 605-645

  Cǎldǎraru, Andrei ^a   Distler, Jacques ^b   Hellerman, Simeon ^c   Pantev, Tony ^d   Sharpe, Eric ^e  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

^d UNIVERSITY OF PENNSYLVANIA   (United States)

^e VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76349089303     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0974-2     Document Type: Article

References (53)

1. Witten E.: Phases of N = 2 theories in two dimensions. Nucl Phys. B 403, 159-222 (1993).
2. Hellerman S., Henriques A., Pantev T., Sharpe E., Ando M.: Cluster decomposition, T-duality, and gerby CFT's. Adv. Theo. Math. Phys. 11, 751-818 (2007).
3. Hori K., Tong D.: Aspects of non-Abelian gauge dynamics in two-dimensional N = (2, 2) theories. JHEP 0705, 079 (2007).
4. Sharpe E.: String orbifolds and quotient stacks. Nucl. Phys. B627, 445-505 (2002).
5. Vafa C., Witten E.: On orbifolds with discrete torsion. J. Geom. Phys. 15, 189-214 (1995).
6. Donagi R., Sharpe E.: GLSMs for partial flag manifolds. J. Geom. Phys. 58, 1662-1692 (2008).
7. Reid, M.: The complete intersection of two or more quadrics. Ph. D. thesis, Trinity College, Cambridge, 1972, available at http://www.warwick.ac.uk/~masda/3folds/qu.pdf.
8. Griffiths P., Harris J.: Principles of Algebraic Geometry. John Wiley & Sons, New York (1978).
9. Clemens H.: Double solids. Adv. in Math. 47, 107-230 (1983).
10. Cynk, S., Meyer, C.: Geometry and arithmetic of certain double octic Calabi-Yau manifolds. http://arxiv.org/abs/math/0304121v1[math.AG], 2003.
11. Cǎldǎraru A., Katz S., Sharpe E.: D-branes, B fields, and Ext groups. Adv. Theor. Math. Phys. 7, 381-404 (2004).
12. 2. http://arxiv.org/abs/math/0512182v1[math.AG], 2005.
13. Gross, M.: Private communication, September 27, 2006.
14. Kuznetsov, A.: Derived categories of quadric fibrations and intersections of quadrics. http://arxiv.org/abs/math/0510670v1[math.AG], 2005.
15. Sharpe E.: D-branes, derived categories, and Grothendieck groups. Nucl. Phys. B561, 433-450 (1999).
16. Douglas M.: D-branes, categories, and N = 1 supersymmetry. J. Math. Phys. 42, 2818-2843 (2001).
17. Sharpe, E.: Lectures on D-branes and sheaves. Writeup of lectures given at the Twelfth Oporto meeting on "Geometry, Topology, and Physics," and at the Adelaide Workshop "Strings and Mathematics 2003,"http://arxiv.org/abs/hep-th/0307245v2, 2003.
18. Pantev, T., Sharpe, E.: Notes on gauging noneffective group actions. http://arxiv.org/abs/hep-th/0502027v2, 2005.
19. Pantev T., Sharpe E.: String compactifications on Calabi-Yau stacks. Nucl. Phys. B733, 233-296 (2006).
20. Pantev T., Sharpe E.: GLSM's for gerbes (and other toric stacks). Adv. Theor. Math. Phys. 10, 77-121 (2006).
21. Sharpe, E.: Derived categories and stacks in physics. http://arxiv. org/abs/hep-th/0608056v2, 2006.
22. Kuznetsov, A.: Homological projective duality. http://arxiv.org/abs/math/0507292v1[math.AG], 2005.
23. Kuznetsov, A.: Homological projective duality for Grassmannians of lines. http://arxiv.org/abs/math/0610957v1[math.AG], 2006.
24. Harris, J.: Algebraic geometry: a first course. Grad. Texts in Math. 133, New York: Springer-Verlag, 1992.
25. Cǎldǎraru, A.: Derived categories of twisted sheaves on elliptic threefolds. http://arxiv.org/abs/math/0012083v3[math.AG], 2001.
26. Cǎldǎraru, A.: N. Addington: Work in progress.
27. Kapustin A., Li Y.: D-branes in Landau-Ginzburg models and algebraic geometry. JHEP 0312, 005 (2003).
28. Kuznetsov, A.: Private communication.
29. Mukai S.: Moduli of vector bundles on K3 surfaces, and symplectic manifolds. Sugaku Expositions 1, 139-174 (1988).
30. Kuznetsov, A.: Private communication, January 29, 2007.
31. Cǎldǎraru, A.: To appear.
32. Sharpe E.: Discrete torsion. Phys. Rev. D68, 126003 (2003).
33. Sharpe E.: Recent developments in discrete torsion. Phys. Lett. B498, 104-110 (2001).
34. Cǎldǎraru, A., Giaquinto, A., Witherspoon, S.: Algebraic deformations arising from orbifolds with discrete torsion. http://arxiv.org/abs/math/0210027v2[math.KT], 2003.
35. Melnikov I., Plesser R.: A-model correlators from the Coulomb branch. JHEP 0602, 044 (2006).
36. Bertram, A.: Private communication, January 5, 2007.
37. Beauville, A.: Complex Algebraic Surfaces. Second edition, Cambridge: Cambridge University Press, 1996.
38. Iyer, J., Simpson, C.: A relation between the parabolic Chern characters of the de Rham bundles. http://arxiv.org/abs/math/0603677v2[math.AG], 2006.
39. Adams A., Polchinski J., Silverstein E.: Don't panic! Closed string tachyons in ALE space-times. JHEP 0110, 029 (2001).
40. Harvey, J., Kutasov, D., Martinec, E., Moore, G.: Localized tachyons and RG flows. http://arxiv.org/abs/hep-th/0111154v2, 2001.
41. Martinec, E., Moore, G.: On decay of K theory. http://arxiv. org/abs/hep-th/0212059v1, 2002.
42. Kuznetsov, A.: Private communication, March 10, 2007.
43. Orlov, D.: Triangulated categories of singularities and D-branes in Landau-Ginzburg models. http://arxiv.org/abs/math/0302304v2[math.AG], 2004.
44. Orlov, D.: Triangulated categories of singularities and equivalences between Landau-Ginzburg models. http://arxiv.org/abs/math/0503630v1[math.AG], 2005.
45. Orlov, D.: Derived categories of coherent sheaves and triangulated categories of singularities. math. AG/0503632.
46. Pantev, T., Sharpe, E.: Work in progress.
47. Guffin, J., Sharpe, E.: To appear.
48. Kontsevich, M.: Course on non-commutative geometry. ENS, 1998 Lecture notes at http://www.math.uchicago.edu/~mitya/langlands/html.
49. Kontsevich, M.: Talk at the "Hodge centennial conference," Edinburgh, 2003.
50. Soibelman, Y.: Lectures on deformation theory and mirror symmetry. IPAM, 2003, http://www.math.ksu.edu/~soibel/ipam-final.ps, 2003.
51. Costello, K.: Topological conformal field theories and Calabi-Yau categories. http://arxiv.org/abs/math/0412149v7[math.QA], 2006.
52. Toën, B., Vaquie, M.: Moduli of objects in dg-categories. http://arxiv.org/abs/math/0503269v5[math.AG], 2007.
53. Bondal A., van den Bergh M.: Generators and representability of functors in commutative and noncommutative geometry. Mosc. Math. J. 3, 1-36 (2003).