arXiv subjects
Publications and source records attributed to Ken Kuwata.
In this paper, we propose a conjecture that clarifies the relationship between the number of degree d elliptic curves in complex four-dimensional projective Fano hypersurfaces and their degree d elliptic Gromov-Witten (GW) invariants. The elliptic GW invariants are computed using the elliptic virtual structure constants proposed in our previous works.
In this paper, we generalize our formalism of the elliptic virtual structure constants to hypersurfaces and complete intersections within certain weighted projective spaces possessing a single K\"ahler class.
In this paper, we propose a method for computing genus 1 Gromov-Witten invariants of Calabi-Yau and Fano projective hypersurfaces using the B-model. Our formalism is applicable to both Calabi-Yau and Fano cases. In the Calabi-Yau case, significant cancellation of terms within our formalism occurs, resulting in an alternative representation of the BCOV-Zinger formula for projective Calabi-Yau hypersurfaces.
In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) and Atiyah-Jeffrey construction. Especially, we construct path-integral representation of Euler number of G(k,N). Our model corresponds to a finite dimensional toy-model of topological Yang-Mills theory which motivated Atiyah-Jeffrey construction. As a by-product, we construct free fermion realization of cohomology ring of G(k,N).
Imanishi, Jinzenji and Kuwata provided a recipe for computing Euler number of Grassmann manifold $G(k,N)$ using physical model and its path-integral [S.Imanishi, M.Jinzenji and K.Kuwata, Journal of Geometry and Physics, Volume 180, October 2022, 104623]. They demonstrated that the cohomology ring of $G(k,N)$ is represented by fermionic variables. In this study, using only fermionic variables, we computed an integral of the Chern classes of the dual bundle of the tautological bundle on $G(k,N)$. In other words, the intersection number of the Schubert cycles is obtained using the fermion integral.
Witten suggested that fixed-point theorems can be derived by the supersymmetric sigma model on a Riemann manifold M with potential term induced from Killing vector on M. One of the well-known fixed-point theorem is the Bott residue formula which represents intersection number of Chern classes of holomorphic vector bundles on a Kahler manifold M as sum of contributions from fixed point sets of a holomorphic vector field K on M. In this paper, we derive the Bott residue formula by using topological sigma model (A-model) that describes dynamics of maps from CP^{1} to M, with potential term induced from the vector field $K$. Our strategy is to restrict phase space of path integral to maps homotopic to constant maps. As an effect of adding a potential term to topological sigma model, we are forced to modify BRST symmetry of the original topological sigma model. Our potential term and BRST symmetry are closely related to the idea used in the paper by Beasley and Witten where potential terms induced from holomorphic section of a holomorphic vector bundle and corresponding supersymmetry are considered.