TITLE

Algebraic Surfaces and Curves with New results on Zariski Pairs

 

ABSTRACT

As part of our research on the classification of algebraic surfaces and curves, we will discuss how the classification problem is related to the theory of Zariski pairs and present some examples demonstrating our progress in this direction.

We also show planar and non-planar degenerations of algebraic surfaces and the calculation of fundamental groups. A few algebraic, geometric, and topological methods and invariants in the classification will be presented, and this includes the necessity of algorithms and software. Some open questions will be presented as well.