Markov fractions and the slopes of the exceptional bundles on \mathbb P²

2025/01/12 by Veselov, A. P.
#11H99 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.06779

Abstract

We show that the Markov fractions introduced recently by Boris Springborn are precisely the slopes of the exceptional vector bundles on \mathbb P² studied in 1980s by Drèzet 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 P² are Markov numbers.

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