- Dirichlet branes and mirror
symmetry with P.Aspinwall, T.Bridgeland, M.Douglas, M.Gross, A.Kapustin, G.Moore, G.Segal, B.Szendroi, P.M.H.Wilson, Clay Mathematics Monographs 4. AMS, Providence, RI, 2009. x+681 pp.
Publications and preprints
- (with J. Green) Reconstructing toric quiver flag varieties from a tilting bundle, to appear European Journal of Mathematics.
- (with Y. Ito and J. Karmazyn) Multigraded linear series and recollement, to appear Mathematische Zeitschrift.
- (with S. Cautis and T. Logvinenko) Derived Reid's recipe for
abelian subgroups of SL(3,ℂ), Journal für die reine und angewandte Mathematik (Crelle's Journal) 727 (2017), 1-48.
- (with A. Bayer and Z. Zhang) Nef divisors for moduli spaces of complexes with compact support, Selecta Mathematica (New Series) 23 (2017), no. 2, 1507-1561.
- (with R. Bocklandt and A. Quintero Vélez) Geometric Reid's recipe for dimer models, Mathematische Annalen 361 (2015), 689-723.
- (with A. Quintero Vélez) Cohomology of wheels on
toric varieties, Hokkaido Mathematical Journal 44 (2015), 47-79.
D. Winn) Mori
Dream Spaces as fine moduli of quiver representations, Journal of Pure and Applied Algebra 217 (2013), 172-189.
- (with A. Quintero Vélez) Cellular resolutions of noncommutative toric algebras from superpotentials, Advances in Mathematics 229 (2012), no. 3., 1516-1554.
- Quiver flag varieties and multigraded linear series, Duke Mathematical Journal 156 (2011), no. 3., 469-500.
- The Special McKay correspondence as an equivalence of derived categories, Quarterly Journal of Mathematics 62 (2011), 573-591.
- (with G. Smith) Projective toric varieties as fine moduli spaces of quiver representations, American Journal of Mathematics 130 (2008), no. 6, 1509-1534.
- (with D. Maclagan and R. Thomas) Moduli of McKay quiver representations II: Grobner basis techniques, Journal of Algebra 316 (2007), no. 2, 514-535.
- (with D. Maclagan) Fiber fans and toric quotients, Discrete and Computational Geometry 37 (2007), no. 2, 251-266.
- (with D. Maclagan and R. Thomas) Moduli of McKay quiver representations I: the coherent component, Proceedings of the London Mathematical Society 95 (2007), no. 1, 179-198.
- An explicit construction of the McKay correspondence for A-Hilb ℂ^3, Journal of Algebra 285 (2005), no. 2, 682-705.
- (with A. Ishii) Flops of G-Hilb and
equivalences of derived categories by variation of GIT quotient, Duke Mathematical Journal 124 (2004), no. 2, 259-307.
- An introduction to motivic integration, In Strings and Geometry, 203-225, Clay Mathematical Proceedings 3, AMS, Providence, RI, 2004.
- (with M. Reid) How to
calculate A-Hilb ℂ^3, In Geometry of
toric varieties, 129--154, Séminaires et Congrès 6, SMF,
- The McKay
correspondence and representations of the McKay quiver, University of Warwick Ph.D thesis, xviii + 134 pp, June 2001.
Published reports and lecture notes
toric geometry, Oberwolfach Reports 9 (2012), no. 2, 1254-1257.
- Toric varieties are fine moduli spaces, Oberwolfach Reports 3 (2006), no. 2, 266-268.
- (for W. Fulton) Enumerative Geometry, Quantum Field Theory, Supersymmetry, and Enumerative Geometry
(IAS/PCMI, V. 11), AMS (2006).
- (for C.H. Clemens) Introduction to Hodge Theory, Appunti dei Corsi Tenuti da Docenti della Scuola. Scuola Normale Superiore, Pisa, 1998. 72 pp.