Maximizing curves viewed as free curves
Alexandru Dimca, Piotr Pokora
TL;DR
This paper explores the relationship between maximizing curves in algebraic surface construction and free plane curves with simple singularities, also examining odd degree curves with maximal Tjurina number.
Contribution
It establishes a direct link between maximizing curves and free plane curves with simple singularities, and investigates properties of odd degree curves with maximal Tjurina number.
Findings
Connected maximizing curves to free curves with simple singularities.
Characterized odd degree curves with maximal Tjurina number.
Provided new insights into algebraic surface Picard numbers.
Abstract
The aim of this paper is to provide a direct link between maximizing curves that occur in the construction of smooth algebraic surfaces having the maximal possible Picard numbers and reduced free plane curves with simple singularities. We also investigate odd degree plane curves with simple singularities having maximal total Tjurina number.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory · Polynomial and algebraic computation