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arXiv · 2501.06779

Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$

A. P. Veselov
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Abstract

We show that the Markov fractions introduced recently by Boris Springborn are precisely the slopes of the exceptional vector bundles on $\mathbb P^2$ studied in 1980s by Dr\`ezet and Le Potier and by Rudakov. In particular, we provide a simpler proof of Rudakov's result claiming that the ranks of the exceptional bundles on $\mathbb P^2$ are Markov numbers.

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A. P. Veselov. 2025-01-12. Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$. https://arxiv.org/abs/2501.06779

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