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.
Roé, J., Supino, P. (2018). Nagata type statements. In Phenomenological Approach to Algebraic Geometry (pp.213-258). WARSZAWA : INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES [10.4064/bc116-8].
Nagata type statements
Paola Supino
2018-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
