An o-minimal Szemer\'edi-Trotter theorem

Saugata Basu; Orit E. Raz

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arXiv · 1611.07362

An o-minimal Szemer\'edi-Trotter theorem

Saugata Basu·Orit E. Raz

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Abstract

We prove an analog of the Szemer\'edi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field $\mathrm{R}$. One new ingredient in the proof is an extension of the well known crossing number inequality for graphs to the case of embeddings in any o-minimal structure over an arbitrary real closed field.

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Saugata Basu, Orit E. Raz. 2016-11-22. An o-minimal Szemer\'edi-Trotter theorem. https://arxiv.org/abs/1611.07362

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