On the joints problem with multiplicities

2014/08/25 by Márton Hablicsek, Hablicsek, Márton · 2 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:52C99 #msc:5A99

paper · pdf · doi:10.48550/arxiv.1408.5791

arxiv created 2014/08/25 · arxiv updated 2014/08/26

Abstract

In this short note we apply a recent theorem of Kollár about the arithmetic genus of curves to give a bound on the number of joints weighted by the multiplicities. This gives an affirmative answer to a conjecture of Carbery in the generic case.

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• A proof of the Multijoints Conjecture and Carbery's generalization
• Generalizations of Joints Problem

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