Gromov-Witten Invariants of Symmetric Products of Projective Space

Moduli spaces;Orbifolds;Mathematics;Science;Mathematics

Silversmith, RobertSpeyer, David E ;

University of Michigan

关键词: Moduli spaces;    Orbifolds;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/138727/rsilvers_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Gromov-Witten invariants are numbers that roughly count curves of a fixed type on an algebraic variety X. For example, for 3 general points and 6 general lines in X=P^3, there are exactly 190 twisted cubics intersecting all of them, so 190 is a Gromov-Witten invariant of P^3. Gromov-Witten invariants appear in algebraic geometry and string theory. In the special case when X is a toric variety, Kontsevich found a method to compute any Gromov-Witten invariant of X. Givental and Lian-Liu-Yau used Kontsevich’s algorithm to prove a mirror theorem, which states that Gromov-Witten invariants of X have an interesting rigid structure predicted by physicists. The main result of this thesis is a mirror theorem for the nontoric orbifold X=Sym^d(P^r), the symmetric product of projective space, which parametrizes unordered d-tuples of points in P^r.