An introduction to enumerative geometry

• Grant number: 18/26163-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2019
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Daniel Levcovitz
• Grantee: Lucas Mioranci
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The goal of this project is to study part of the book "3264 and All That - A Second Course in Algebraic Geometry" by David Eisenbud and Joe Harris as an introduction to Enumerative Geometry.We plan to follow the reference above as a source of theory and exercises. More precisely, we have in mind to read the five first chapters from the book, which cover the basic material. Afterward, we intend to skip to chapter 10 (Segre classes and varieties of linear spaces) in order to study the celebrated Alexander and Hirschowitz's theorem on the classification of defective Veronese varieties. This theorem is going to be the main topic on the Master's dissertation. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MIORANCI, Lucas. On defective Veronese varieties and the Alexander-Hirschowitz theorem. 2019. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.