Open Access
Coordinate Change of Gauss-Manin System and Generalized Mirror Transformation
Masao Jinzenji
- Vol. 619, pp 1-19
TLDR
In this article, the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces was derived as an effect of coordinate change of the virtual Gauss-Manin system.Abstract:
In this paper, we explicitly derive the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces, proposed in our previous article, as an effect of coordinate change of the virtual Gauss-Manin system.read more
Citations
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Variétés rationnellement connexes sur un corps algébriquement clos
TL;DR: In this paper, the notes of a mini-cours on rationnellement connexite connexes are presented. But they do not mention the conjecture of connexité rationnelle of Shokurov par Hacon and Kernan.
References
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Gromov-Witten classes, quantum cohomology, and enumerative geometry
Maxim Kontsevich,Yu. I. Manin +1 more
TL;DR: In this paper, the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry are discussed, and an axiomatic treatment of Gromov-Witten classes and their properties for Fano varieties are discussed.
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Enumeration of Rational Curves Via Torus Actions
TL;DR: In this paper, an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry is made. But this work is restricted to the case of a single curve.
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Equivariant Gromov-Witten invariants
TL;DR: In this article, the equivariant counterpart to the Gromov-Witten (GW) theory is proposed for intersection theory on spaces of (pseudo-) holomorphic curves in (almost-) Kahler manifolds.
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Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
TL;DR: For any smooth complex projective variety $X$ and any smooth very ample hypersurface $Y\subset X, this paper developed the technique of genus zero relative Gromov-Witten invariants of $Y$ in X$ in algebro-geometric terms and proved an equality of cycles in the Chow groups of the moduli spaces of relative stable maps.
Journal ArticleDOI
Quantum D-modules and generalized mirror transformations
TL;DR: In this paper, the authors showed that the equivariant Floer cohomology can reconstruct the big quantum D-module under certain conditions on the ambient toric variety, based on a generalized mirror transformation first observed by Jinzenji in low degrees.