Quantum Cohomology of Complete Intersections
Arnaud Beauville (1997)
Recherche Coopérative sur Programme n°25
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Displaying similar documents to “Quantum cohomology and its application.”
Quantum Cohomology of Complete Intersections
An introduction to quantum sheaf cohomology
Eric Sharpe (2011)
Annales de l’institut Fourier
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In this note we review “quantum sheaf cohomology,” a deformation of sheaf cohomology that arises in a fashion closely akin to (and sometimes generalizing) ordinary quantum cohomology. Quantum sheaf cohomology arises in the study of (0,2) mirror symmetry, which we review. We then review standard topological field theories and the A/2, B/2 models, in which quantum sheaf cohomology arises, and outline basic definitions and computations. We then discuss (2,2) and (0,2) supersymmetric Landau-Ginzburg...
The cohomology of holomorphic self maps of the Riemann sphere.
John W. Havlicek (1995)
Mathematische Zeitschrift
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On quantum de Rham cohomology theory.
Cao, Huai-Dong, Zhou, Jian (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Nonclassical descriptions of analytic cohomology
Bailey, Toby N., Eastwood, Michael G., Gindikin, Simon G.
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Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [, and , J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes...
Quantum cohomology of flag manifolds and quantum Toda lattices.
Kim, Bumsig (1999)
Annals of Mathematics. Second Series
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Cohomology Groups of Locally q-Complete Morphisms with r-Complete Base.
Viorel Vâjâitu (1996)
Mathematica Scandinavica
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Dimensions of Sheaf Cohomology Groups under Holomorphic Deformation.
Yum-Tong SIU (1971)
Mathematische Annalen
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Holomorphic Poisson Cohomology
Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)
Complex Manifolds
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Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients...
A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds
Yat Sun Poon, John Simanyi (2017)
Complex Manifolds
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A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bicomplex where one of the two operators is the classical მ̄-operator, while the other operator is the adjoint action of the Poisson bivector with respect to the Schouten-Nijenhuis bracket. The first page of the associated spectral sequence is the Dolbeault cohomology with coefficients in the sheaf of germs of holomorphic polyvector fields. In this note, the authors investigate the conditions...
Operations and quantum doubles in complex oriented cohomology theory.
Buchstaber, Victor M., Ray, Nigel (1999)
Homology, Homotopy and Applications
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Quantum Cohomology and Periods
Hiroshi Iritani (2011)
Annales de l’institut Fourier
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In a previous paper, the author introduced an integral structure in quantum cohomology defined by the -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism...