Convergence of quantum cohomology by quantum Lefschetz
By H. Iritani. 2005
83 citations recorded by the source corpus.
Abstract Quantum Lefschetz theorem by Coates and Givental [T. Coates, A. B. Givental, Quantum Riemann-Roch, Lefschetz and Serre, math.AG/0110142.] gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle ℒ on X. We prove the convergence of the twisted theory under the assumption that the genus 0 theory for original X converges. As a byproduct, we prove the semisimplicity and the Virasoro conjecture for the Gromov-Witten theories of (not necessarily Fano) projective toric manifolds.
View Paper: https://www.semanticscholar.org/paper/cb171a0c4ed94a42312385e2bef34c22d124b7dd
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- Hsian-Hua Tseng
- Christopher Woodward
- T. Milanov
- Daewoong Cheong
- H. Iritani
- Chiu-Chu Melissa Liu
- Alexander Givental
- Ionut Ciocan-Fontanine
Citations in the corpus
- Lagrangian Floer theory on compact toric manifolds II: bulk deformations (2008, methodology): “anges. In other words, the story over Q[[q1,··· ,qm−n]] corresponds to studying all the symplectic structures simultaneously, while the story over Λ focuses on one particular symplectic structure. In [Iri2] Corollary 5.12, Iritani proved semi-simplicity of quantum cohomology ring of toric manifold w”
- Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms (2010, methodology): “4, part (i) follows directly from a theorem of Iritani [33] and Theorem 7.”
- QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, methodology): “In this way one obtains formula similar to the “mirror formulas” of Givental [18], Lian-Liu-Yau [28], Iritani [22] and others for localized graph potentials [18] in the toric case, but now for arbitrary geometric invariant theory quotients.”
- The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies (2008, background): “They belong to the Fock space B, which is an infinite dimensional vector space described as follows: if we pick a trivialization of the tangent bundle TM GM H, corresponding to a choice of a flat coordinate system on M (here H is an arbitrary fixed tangent space of M), then B is a certain…”