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On line arrangements with odd multiplicities

Marco Golla

Abstract

We give restrictions on the weak combinatorics of line arrangements with singular points of odd multiplicity using topological arguments on locally-flat spheres in 4-manifolds. As a corollary, we show that there is no line arrangement comprising 13 lines and with only triple points.

On line arrangements with odd multiplicities

Abstract

We give restrictions on the weak combinatorics of line arrangements with singular points of odd multiplicity using topological arguments on locally-flat spheres in 4-manifolds. As a corollary, we show that there is no line arrangement comprising 13 lines and with only triple points.
Paper Structure (2 sections, 4 theorems, 9 equations)

This paper contains 2 sections, 4 theorems, 9 equations.

Table of Contents

  1. Notation and background
  2. Acknowledgements

Key Result

Theorem 1

Let $L$ be a locally-flat line arrangement of degree $d$ with only triple points. Then $d \equiv 1, 3, 9, 19 \pmod{24}$.

Theorems & Definitions (8)

  • Theorem 1
  • Corollary 2
  • Theorem 3
  • Lemma 4
  • proof
  • proof : Proof of Theorem \ref{['t:odd']}
  • Remark 5
  • proof : Proof of Theorem \ref{['t:main']}