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This paper contains some applications of Bridgeland-Douglas stability conditions on triangulated categories, and Joyce's work on counting invariants of semistable objects, to the study of birational geometry.
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Mumford-Thaddeus principle on the moduli space of vector bundles on an algebraic surface
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On the topology of birational minimal models
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Birational Calabi-Yau n n -folds have equal Betti numbers
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Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
V. V. Batyrev · 1999
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Topological Strings and Spinning Black Holes
S. Katz, A.Klemm, and C.Vafa · 1999
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D-branes, categories and N = 1 {N}=1 supersymmetry
M. Douglas · 2001
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Relative Lefschetz actions and BPS state counting
S. Hosono, M. Saito, and A. Takahashi · 2001
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Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds
A.-M. Li and Y. Ruan · 2001
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Flops and derived categories
T. Bridgeland · 2002
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Stringy Hodge numbers and p p -adic Hodge theory
T. Ito · 2004
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Three dimensional flops and noncommutative rings
M. Van den Bergh · 2004
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Some remarks on Gopakumar-Vafa invariants
A. Schwarz and I. Shapiro · 2005
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Configurations in abelian categories I. Basic properties and moduli stack
D. Joyce · 2006
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Moduli of complexes on a proper morphism
M. Lieblich · 2006
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Derived Hall algebras
B. To e ¨ \ddot{\textrm{e}} n · 2006
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Configurations in abelian categories II. Ringel-Hall algebras
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J-C. Chen · 2002
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Motivic integration, quotient singularities and the McKay correspondence
J. Denef and F. Loeser · 2002
Cited alongside, same era.
Dirichlet branes, homological mirror symmetry, and stability
M. Douglas · 2002
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Twisted jets, motivic measures and orbifold cohomology
T. Yasuda · 2003
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The universal euler characteristic for varieties of characteristic zero
F. Bittner · 2004
Cited alongside, same era.
Donaldson-Thomas invariants via microlocal geometry
K. Behrend
Cited in the paper.
D. Joyce · 2007
Closest in time.
Configurations in abelian categories III. Stability conditions and identities
D. Joyce · 2007
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Motivic invariants of Artin stacks and ‘stack functions’
D. Joyce · 2007
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Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
D. Joyce · 2007
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Configurations in abelian categories IV. Invariants and changing stability conditions
D. Joyce · 2008
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