Hilbert's theorem: free resolution via syzygy module

• Grant number: 16/22968-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2017
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eliris Cristina Rizziolli
• Grantee: Rodrigo de Almeida Rosa
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The central objective of this project is to study the Hilbert Theorem via Syzygy Modules, also known as Hilbert's Syzygy Theorem. This result deals with the existence of a free resolution for finitely generated R modules, where R is a ring of polynomials in a field K in the variables X_1, X_2, ..., X_n. In addition, we intend to apply this theory to explore examples using the free SINGULAR program. (AU)