Divisorial instability and Vojta's Main Conjecture for \ℚ-Fano\n varieties

2019/01/23 by Nathan Grieve, Grieve, Nathan
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.07942

openalex publication_date 2019/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Diophantine arithmetic properties of birational divisors in\nconjunction with concepts that surround \K-stability for Fano\nvarieties. There is also an interpretation in terms of the barycentres of\nNewton-Okounkov bodies. Our main results show how the notion of divisorial\ninstability, in the sense of K. Fujita, implies instances of Vojta's Main\nConjecture for Fano varieties. A main tool in the proof of these results is an\narithmetic form of Cartan's Second Main Theorem that has been obtained by M. Ru\nand P. Vojta.\n

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