Linear system of cubic forms with base locus of 5 points

Abstract

Studying a variety through a linear system of homogenous forms with a base locus is a method that has many advantages not only for understanding important geometric properties but also the ability to accurately evaluate many invariants of the variety. This paper aims to study linear systems of cubic forms through 5 points in the projective plane with many configurations. Many interesting and profound properties of surfaces have been discovered through their corresponding linear systems. These results not only enrich correspondence theory in algebraic geometry and computational algebra but also promise to provide methods and tools for applications in the fields of information technology and other technologies.

Keywords

• varieties and morphism
• computational algebra
• singularity
• linear system
• blowing-up