TAILIEUCHUNG - Đề tài " Higher genus GromovWitten invariants as genus zero invariants of symmetric products "

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S g+1 (X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the GromovWitten invariants of a point. 1. Introduction Let X be a smooth projective variety. The genus 0 Gromov-Witten invariants of X satisfy relations which imply that they can be completely encoded in the structure of a Frobenius manifold on the cohomology H ∗ (X, C). . | Annals of Mathematics Higher genus Gromov-Witten invariants as genus zero invariants of symmetric products By Kevin Costello Annals of Mathematics 164 2006 561 601 Higher genus Gromov-Witten invariants as genus zero invariants of symmetric products By Kevin Costello Abstract I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack Sg 1 X . When X is a point the latter are structure constants of the symmetric group and we obtain a new way of calculating the Gromov-Witten invariants of a point. 1. Introduction Let X be a smooth projective variety. The genus 0 Gromov-Witten invariants of X satisfy relations which imply that they can be completely encoded in the structure of a Frobenius manifold on the cohomology H X C . In this paper I prove a formula which expresses the descendent genus g Gromov-Witten invariants of a smooth projective variety X in terms of the descendent genus 0 invariants of the symmetric product stack Sg 1X. The latter are encoded in a Frobenius manifold structure on the orbifold cohomology group HOrb Sg 1 X C . This implies that the Gromov-Witten invariants of X at all genera are described by a sequence of Frobenius manifold structures on the homogeneous components of the Fock space F Sym H X C C iC i d 0H rb Sd X C . Standard properties of genus 0 invariants such as associativity when applied to the symmetric product stacks SdX yield implicit relations among higher-genus Gromov-Witten invariants of X . When X is a point the symmetric product is the classifying stack BSd of the symmetric group. The Frobenius manifold associated to the genus 0 invariants of BSd is in fact a Frobenius algebra which is the center of the group algebra of the symmetric group C SdA. Our result therefore gives a new way of expressing the integrals of tautological classes on Mg n in terms of structure constants of C Sd . 562 KEVIN COSTELLO More generally the .

• Thạc sĩ - Tiến sĩ - Cao học
• Higher genus
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• công trình toán học
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center