Introduction to complex analytical geometry

• Grant number: 17/19553-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2017
• End date: May 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Felipe Espreafico Guelerman Ramos
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM
• Associated scholarship(s): 18/14008-7 - Tjurina transform and determinantal singularities, BE.EP.IC

Abstract

Subsets of complex spaces, affine or projective spaces defined by polynomial equations are studied in Algebraic Geometry. Examples are quadrics, cubics, etc. In Analytic Geometric the first objects of investigations are subsets of these spaces defined by analytic equations. As every polynomial is an analytic function, this set of objects contains the first one. Furthermore, the study of analytic sets allows a deeper investigation of singularities. (AU)