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2 results on '"3-Syzygy curves"'

1. On 3-syzygy and unexpected plane curves.

Author

Malara, Grzegorz, Pokora, Piotr, and Tutaj-Gasińska, Halszka

Abstract

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study 3-syzygy curve arrangements and we present examples that admit unexpected curves. [ABSTRACT FROM AUTHOR]

Published
2021
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2. On $3$-syzygy and unexpected plane curves

Author

Grzegorz Malara, Piotr Pokora, and Halszka Tutaj-Gasińska

Subjects
Pure mathematics, Plane curve, Hyperbolic geometry, 0102 computer and information sciences, Algebraic geometry, Commutative Algebra (math.AC), 01 natural sciences, unexpected curves, Mathematics - Algebraic Geometry, FOS: Mathematics, 0101 mathematics, Algebraic Geometry (math.AG), Topology (chemistry), Complex projective plane, Mathematics, Projective geometry, Hilbert's syzygy theorem, conic arrangements, 010102 general mathematics, line arrangements, Mathematics - Commutative Algebra, almost freeness, 14N20, 14C20, 32S22, Differential geometry, 010201 computation theory & mathematics, nearly freeness, 3-Syzygy curves, Geometry and Topology
Abstract

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study $3$-syzygy arrangements and we present examples that admit unexpected curves., Comment: 19 pages, one figure, version after referee's remarks

Published
2021

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