Maximizing curves viewed as free curves

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.

arXiv comment28 pages, this is the final version incorporating referees remark. To appear in International Mathematics Research Notices

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Cited by in corpus (2)

• Construction of free curves by adding lines to a given curve
• On free and nearly free arrangements of conics admitting certain $\mathrm{ADE}$ singularities