Coordinate Change of Gauss-Manin System and Generalized Mirror Transformation
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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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.
Journal ArticleDOI
Convergence of quantum cohomology by quantum Lefschetz
TL;DR: In this paper, the convergence of the twisted theory under the assumption that the genus 0 Gromov-Witten theory for original X converges has been proved for projective toric manifolds.
Journal ArticleDOI
Extending the Picard-Fuchs system of local mirror symmetry
Brian Forbes,Masao Jinzenji +1 more
TL;DR: In this paper, an extended set of differential operators for local mirror symmetry was proposed, and a conjecture for intersection theory for such a set of operators was uncovered, along with operators on several examples of type X =KS through similar techniques.
Journal ArticleDOI
J functions, non-nef toric varieties and equivariant local mirror symmetry of curves
Brian Forbes,Masao Jinzenji +1 more
TL;DR: In this article, the authors provide a straightforward computational scheme for the equivariant local mirror symmetry of curves, i.e. mirror symmetry for for k ≥ 1, and detail related methods for dealing with mirror symmetry in non-nef toric varieties, based on the theorems of Refs. 2 and 13.
Posted Content
Lines, conics, and all that
TL;DR: A survey on Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc. is given in this article.
References
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Journal ArticleDOI
Gromov-Witten classes, quantum cohomology, and enumerative geometry
Maxim Kontsevich,Yu. I. Manin +1 more
TL;DR: In this article, 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.
Book ChapterDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
Mirror Principle II
TL;DR: The authors generalize the results in Mirror Principle I to a class of balloon manifolds and extend them to projective manifolds without the convexity assumption, and show that these manifolds can be expressed as convex projective projective models.
Journal ArticleDOI
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.