start-ver=1.4 cd-journal=joma no-vol=77 cd-vols= no-issue=2 article-no= start-page=449 end-page=482 dt-received= dt-revised= dt-accepted= dt-pub-year=2025 dt-pub=202504 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Period integrals (Givental's I-function) of Calabi?Yau hypersurface in CPN?1 as generating functions of intersection numbers on the moduli space of quasimaps en-subtitle= kn-subtitle= en-abstract= kn-abstract=In this paper, we derive the generalized hypergeometric functions (period integrals) used in mirror computation of Calabi?Yau hypersurface in CPN?1 as generating functions of intersection numbers on the moduli space of quasimaps from CP1 with 2+1 marked points to CPN?1. en-copyright= kn-copyright= en-aut-name=JINZENJIMasao en-aut-sei=JINZENJI en-aut-mei=Masao kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=MATSUZAKAKohki en-aut-sei=MATSUZAKA en-aut-mei=Kohki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil=Department of Mathematics, Okayama University kn-affil= affil-num=2 en-affil=Faculty of Integrated Media, Ikueikan University kn-affil= en-keyword=generalized hypergeometric functions kn-keyword=generalized hypergeometric functions en-keyword=Givental's I-function kn-keyword=Givental's I-function en-keyword=moduli space of quasimaps kn-keyword=moduli space of quasimaps END start-ver=1.4 cd-journal=joma no-vol=2024 cd-vols= no-issue=12 article-no= start-page=135 end-page= dt-received= dt-revised= dt-accepted= dt-pub-year=2024 dt-pub=20241217 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Elliptic virtual structure constants and generalizations of BCOV-Zinger formula to projective Fano hypersurfaces en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=JinzenjiMasao en-aut-sei=Jinzenji en-aut-mei=Masao kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=KuwataKen en-aut-sei=Kuwata en-aut-mei=Ken kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil=Department of Mathematics, Okayama University kn-affil= affil-num=2 en-affil=Department of General Education, National Institute of Technology, Kagawa College kn-affil= en-keyword=Nonperturbative Effects kn-keyword=Nonperturbative Effects en-keyword=String Duality kn-keyword=String Duality en-keyword=Topological Field Theories kn-keyword=Topological Field Theories en-keyword=Topological Strings kn-keyword=Topological Strings END start-ver=1.4 cd-journal=joma no-vol=47 cd-vols= no-issue=2 article-no= start-page=162 end-page=177 dt-received= dt-revised= dt-accepted= dt-pub-year=2024 dt-pub=202406 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Generalized hypergeometric functions for degree k hypersurface in CPN-1 and intersection numbers of moduli space of quasimaps from CP1 with two marked points to CPN-1 en-subtitle= kn-subtitle= en-abstract= kn-abstract=In this paper, we derive the generalized hypergeometric functions used in mirror computation of degree k hypersurface in CPN-1 as generating functions of intersection numbers of the moduli space of quasimaps from CP1 with two marked points to CPN-1. en-copyright= kn-copyright= en-aut-name=JinzenjiMasao en-aut-sei=Jinzenji en-aut-mei=Masao kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=MatsuzakaKohki en-aut-sei=Matsuzaka en-aut-mei=Kohki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= affil-num=1 en-affil=Department of Mathematics, Okayama University kn-affil= affil-num=2 en-affil=Faculty of Integrated Media, Ikueikan University kn-affil= en-keyword=Givental's I-function kn-keyword=Givental's I-function en-keyword=Generalized hypergeometric series kn-keyword=Generalized hypergeometric series en-keyword=Moduli space of quasimaps kn-keyword=Moduli space of quasimaps en-keyword=Intersection number kn-keyword=Intersection number END start-ver=1.4 cd-journal=joma no-vol=34 cd-vols= no-issue=02 article-no= start-page=2350006 end-page= dt-received= dt-revised= dt-accepted= dt-pub-year=2023 dt-pub=20230203 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Geometrical proof of generalized mirror transformation of projective hypersurfaces en-subtitle= kn-subtitle= en-abstract= kn-abstract=In this paper, we propose a geometrical proof of the generalized mirror transformation of genus 0 Gromov?Witten invariants of degree k hypersurface in CPN-1 en-copyright= kn-copyright= en-aut-name=JinzenjiMasao en-aut-sei=Jinzenji en-aut-mei=Masao kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil=Department of Mathematics, Okayama University kn-affil= en-keyword=Mirror symmetry kn-keyword=Mirror symmetry en-keyword=moduli space of quasimaps kn-keyword=moduli space of quasimaps en-keyword=excess intersection kn-keyword=excess intersection en-keyword=generalized mirror transformation kn-keyword=generalized mirror transformation END start-ver=1.4 cd-journal=joma no-vol=180 cd-vols= no-issue= article-no= start-page=104623 end-page= dt-received= dt-revised= dt-accepted= dt-pub-year=2022 dt-pub=202210 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Evaluation of Euler number of complex Grassmann manifold G(k,N) via Mathai-Quillen formalism en-subtitle= kn-subtitle= en-abstract= kn-abstract=In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k, N) by using Mathai-Quillen formalism (MQ formalism) [9] and Atiyah-Jeffrey construc-tion [1]. 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). en-copyright= kn-copyright= en-aut-name=ImanishiShoichiro en-aut-sei=Imanishi en-aut-mei=Shoichiro kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=JinzenjiMasao en-aut-sei=Jinzenji en-aut-mei=Masao kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= en-aut-name=KuwataKen en-aut-sei=Kuwata en-aut-mei=Ken kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=3 ORCID= affil-num=1 en-affil=Division of Mathematics, Graduate School of Science, Hokkaido University kn-affil= affil-num=2 en-affil=Department of Mathematics, Okayama University kn-affil= affil-num=3 en-affil=Department of General Education, National Institute of Technology, Kagawa College kn-affil= en-keyword=Supersymmetry kn-keyword=Supersymmetry en-keyword=Topological Yang-Mills theory kn-keyword=Topological Yang-Mills theory en-keyword=Schubert calculus kn-keyword=Schubert calculus en-keyword=Grassmann manifold kn-keyword=Grassmann manifold en-keyword=Grassmann variable kn-keyword=Grassmann variable END