Geometria enumerativa via invariantes de Gromov-Witten e mapas estáveis

• Autor(a) principal: Santos, Renan da Silva
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/12544
• topic: Invariantes de Gromov-Witten; Mapas estáveis; Curvas racionais

In this work, I present the Gromov-Witten theory, quantum cohomology and stable maps and use these tools to obtain some enumerative results. In particular, I proof the Kontsevich formula to projective rational plane curves of degree d. I do an introductory study of Mumford-Knudsen spaces and construct the Kontsevich spaces in order to define gromov-witten invariants. These are used to define the quantum cohomology ring. Next, I apply the general theory to the case of the projective plane and, using the the associativity of the quantum product, I obtain the Kontsevich formula. I also study the boundary of the modulli space of stable maps and describe its Picard group. Following the ideas of Pandharipand, especially the algorithm he developed, I calculate some characteristic numbers of curves in the projective space.