Hall algebras and curve-counting invariants
By T. Bridgeland. 2010
157 citations recorded by the source corpus.
We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions of rational functions.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2f314605576d7881a104b1145156e6ec48624387
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In Geometry and Topology
- Yukinobu Toda
- D. Joyce
- T. Bridgeland
- Yinan Song
- Aaron Pixton
- R. Pandharipande
- Emanuele Macrì
- Arend Bayer
In Mathematical Physics
- Yukinobu Toda
- D. Joyce
- T. Bridgeland
- Aaron Pixton
- Yinan Song
- R. Pandharipande
- Arend Bayer
- Emanuele Macrì
Citations in the corpus
- Gromov-Witten/pairs correspondence for the quintic 3-fold (2012, methodology): “Similarly, in Gromov-Witten theory, we have the determination ZGW(T ⋆ 5 ) Ã Z ′ GW(T ⋆ 4 /S4), and Z ′ GW(P [4, 5]/S4) .”
- Stability conditions and curve counting invariants on Calabi–Yau 3-folds (2011, background): “ects in the derived category is locally written as a critical locus of some holomorphic function up to gauge action. The precise statement is formulated in [35, Conjecture 4.3]. On the other hand, in [9], Bridgeland proves Theorem 3.11 without relying [6], using the arguments different to ours. The i”
- An introduction to motivic Hall algebras (2010, methodology): “This material will be used in Bridgeland (2011) [3] to prove some basic properties of Donaldson–Thomas curve-counting invariants on Calabi–Yau threefolds.”
- A theory of generalized Donaldson–Thomas invariants (2008, background): “Bridgeland [12] also proves the correspondence assuming conjectures in [63].”