Projective toric varieties as fine moduli spaces of quiver representations

American Journal of Mathematics

Volumn 130, Issue 6, 2008, Pages 1509-1534

  Craw, Alastair ^a   Smith, Gregory G ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58049157396     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.0.0027     Document Type: Article

References (28)

1. K. Altmann and L. Hille, Strong exceptional sequences provided by quivers, Algebr. Represent. Theory 2 (1999), no. 1, 1-17.
2. I Assem, D. Simson, and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Vol. 1. Techniques of Representation Theory, London Math. Soc. Stud. Texts, Vol. 65, Cambridge University Press, Cambridge, 2006.
3. D. Bayer, S. Popescu, and B. Sturmfels, Syzygies of unimodular Lawrence ideals, J. Reine Angew. Math. 534 (2001), 169-186.
4. A. Bergman and N. J. Proudfoot, Moduli spaces for Bondal quivers, UTTG-16-05, available at arXiv:math.AG/0512166; Pacific J. Math. (to appear).
5. A. Bigatti, R. La Scala, and L. Robbiano, Computing toric ideals, J. Symbolic Comput. 27 (1999), no. 4, 351-365.
6. N. Biggs, Algebraic Graph Theory, 2nd ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1993.
7. L. J. Billera, I. M. Gel'fand, and B. Sturmfels, Duality and minors of secondary polyhedra, J. Combin. Theory Ser. B 57 (1993), no. 2, 258-268.
8. A. I. Bondal, Representations of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 1, 25-44.
9. D. A. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), no. 1, 17-50.
10. -. The functor of a smooth toric variety, Tohoku Math. J. (2) 47 (1995), no. 2, 251-262.
11. A. Craw, D. Maclagan, and R. Thomas, Moduli of McKay quiver representations I: the coherent component, Proc. London Math. Soc. (3) 95 (2007), no. 1, 179-198.
12. I. V. Dolgachev and Y. Hu, Variation of geometric invariant theory quotients, Inst. Hautes Études Sci. Publ. Math. (1998), 87, 5-56.
13. D. R. Grayson and M. E. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2.
14. C. Greene and T. Zaslavsky, On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs, Trans. Amer. Math. Soc. 280 (1983), no. 1, 97-126.
15. W. Fulton, Introduction to Toric Varieties, Ann. of Math. Stud., vol. 131, Princeton University Press, Princeton, NJ, 1993.
16. M. Hering, H. Schenck, and G. G. Smith, Syzygies, multigraded regularity and toric varieties, Compositio Math. 142 (2006), no. 6, 1499-1506.
17. L. Hille, Toric Quiver Varieties, Algebras and Modules, II (Geiranger, 1996), CMS Conf. Proc., vol. 24, Amer. Math. Soc., Providence, RI, 1998, pp. 311-325.
18. L. Hille and M. Perling, A counterexample to King's conjecture, Compositio. Math. 142 (2006), no. 6, 1507-1521.
19. T. Kajiwara, The functor of a toric variety with enough invariant effective Cartier divisors, Tohoku Math. J. (2) 50 (1998), no. 1, 139-157.
20. Y. Kawamata, Derived categories of toric varieties, Michigan Math. J. 54 (2006), no. 3, 517-535.
21. A. D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2) 45 (1994), no. 180, 515-530.
22. -. Tilting bundles on some rational surfaces (1997), available at http.//www.maths. bath.ac.uk/̃masadk/papers/.
23. D. Maclagan and G .G. Smith, Multigraded Castelnuovo-Mumford regularity, J. Reine Angew. Math. 571 (2004), 179-212.
24. M. Mustaţǎ, Vanishing theorems on toric varieties, Tohoku Math. J. (2) 54 (2002), no. 3, 451-470.
25. T. Oda, Convex Bodies and Algebraic Geometry, Ergeb. Math. Grenzgeb. (3), vol. 15, Springer-Verlag, Berlin, 1988.
26. A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons Ltd., Chichester, 1986.
27. B. Sturmfels, Gröbner Bases and Convex Polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996.
28. M. Thaddeus, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996), no. 3, 691-723.