63 research outputs found
Construction of Free Energy of Calabi-Yau manifold embedded in via Torus Actions
We calculate correlation functions of topological sigma model (A-model) on
Calabi-Yau hypersurfaces in using torus action method. We also
obtain path-integral represention of free energy of the theory coupled to
gravity.Comment: 30 page
Gauss-Manin System and the Virtual Structure Constants
In this paper, we discuss some applications of Givental's differential
equations to enumerative problems on rational curves in projective
hypersurfaces. Using this method, we prove some of the conjectures on the
structure constants of quantum cohomology of projective hypersurfaces, proposed
in our previous article. Moreover, we clarify the correspondence between the
virtual structure constants and Givental's differential equations when the
projective hypersurface is Calabi-Yau or general type.Comment: 25 pages, Latex, references added, minor errors are correcte
Geometrical Proof of Generalized Mirror Transformation of Projective Hypersurfaces
In this paper, we outline geometrical proof of the generalized mirror
transformation of genus 0 Gromov-Witten invariants of degree k hypersurface in
CP^{N-1}.Comment: 10 pages, minor errors are corrected, appendix is added, Introduction
is expanded, references are adde
Coordinate Change of Gauss-Manin System and Generalized Mirror Transformation
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.Comment: 19 pages, latex, minor errors are corrected, discussions in Section 4
are refine
Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model
In this paper, we propose a geometrical approach to mirror computation of
genus 0 Gromov-Witten invariants of CP^2. We use multi-point virtual structure
constants, which are defined as intersection numbers of a compact moduli space
of quasi maps from CP^1 to CP^2 with 2+n marked points. We conjecture that some
generating functions of them produce mirror map and the others are translated
into generating functions of Gromov-Witten invariants via the mirror map. We
generalize this formalism to open string case. In this case, we have to
introduce infinite number of deformation parameters to obtain results that
agree with some known results of open Gromov-Witten invariants of CP^2. We also
apply multi-point virtual structure constants to compute closed and open
Gromov-Witten invariants of a non-nef hypersurface in projective space. This
application simplifies the computational process of generalized mirror
transformation.Comment: 26 pages, Late
Completion of the Conjecture: Quantum Cohomology of Fano Hypersurfaces
In this paper, we propose the formulas that compute all the rational
structural constants of the quantum K\"ahler sub-ring of Fano hypersurfaces.Comment: 19pages, Latex, minor changes in English, some formulas are adde
Generalization of Calabi-Yau/Landau-Ginzburg correspondence
We discuss a possible generalization of the Calabi-Yau/Landau-Ginzburg
correspondence to a more general class of manifolds. Specifically we consider
the Fermat type hypersurfaces : in for various values of k and N. When k<N, the 1-loop beta function of
the sigma model on is negative and we expect the theory to have a mass
gap. However, the quantum cohomology relation
suggests that in addition to the massive
vacua there exists a remaining massless sector in the theory if k>2. We assume
that this massless sector is described by a Landau-Ginzburg (LG) theory of
central charge with N chiral fields with U(1) charge . We
compute the topological invariants (elliptic genera) using LG theory and
massive vacua and compare them with the geometrical data. We find that the
results agree if and only if k=even and N=even.
These are the cases when the hypersurfaces have a spin structure. Thus we
find an evidence for the geometry/LG correspondence in the case of spin
manifolds.Comment: 19 pages, Late
Moduli Space of Quasi-Maps from P^{1} with Two Marked Points to P(1,1,1,3) and j-invariant
In this paper, we construct toric data of moduli space of quasi maps of
degree from P^{1} with two marked points to weighted projective space
P(1.1,1,3). With this result, we prove that the moduli space is a compact toric
orbifold. We also determine its Chow ring. Moreover, we give a proof of the
conjecture proposed by Jinzenji that a series of intersection numbers of the
moduli spaces coincides with expansion coefficients of inverse function of
-log(j(tau)).Comment: 22 pages, minor errors are corrected, references are added, some
comments are added in Introductio
On Quantum Cohomology Rings for Hypersurfaces in
Using the torus action method, we construct one variable polynomial
representation of quantum cohomology ring for degree hypersurface in
. The results interpolate the well-known result of model
and the one of Calabi-Yau hypersuface in . We find in
case, principal relation of this ring have very simple form compatible with
toric compactification of moduli space of holomorphic maps from to
.Comment: 32 pages, Revised versio
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