2017/07/03 by Joaquím Roé, Roé, Joaquim, Paola Supino +1
Computer Science · Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cancer Treatment and Pharmacology #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1707.00583
openalex publication_date 2017/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nagata solved Hilbert's 14-th problem in 1958 in the negative. The solution naturally lead him to a tantalizing conjecture that remains widely open after more than half a century of intense efforts. Using Nagata's theorem as starting point, and the conjecture, with its multiple variations, as motivation, we explore the important questions of finite generation for invariant rings, for support semigroups of multigraded algebras, and for Mori cones of divisors on blown up surfaces, and the rationality of Waldschimdt constants. Finally we suggest a connection between the Mori cone of the Zariski-Riemann space and the continuity of the Waldschmidt constant as a function on the space of valuations.