… X defined by plane divisorial valuations ν of the quotient field of the local ring R at a closed
… cone of X is closed and its Cox ring finitely generated. Equivalent conditions to the fact that ν …

… We consider surfaces X defined by plane divisorial valuations \(\nu \) of the quotient field of
the local ring R at a closed point p of the projective plane \(\mathbb {P}^2\) over an arbitrary …

… Moreover, the language of bunched rings extends basic … Generalizing the case of a toric
variety, we describe the Cox ring … In general, the Cox sheaf is not a sheaf of divisorial algebras. …

… system of parameters for the rings R1,R2,...,RN ,... given by the blow-ups sequence π (4).
Next we describe this concept; an alternative version for divisorial valuations can be found in […

… In this sense, the valuation cone V is related to the failure of the C -algebra Γ ( G / H , O G /
H … We will state a result about the valuation cone which uses tropical algebraic geometry. An …

We define the equivariant Cox ring of a normal variety with algebraic group action. We study
algebraic and geometric aspects of this object and show how it is related to the ordinary …

… When considering a divisorial valuation of X, we denote by ϕC the germ of a curve C on X
at the point p. Additionally, ϕl denotes an analytically irreducible germ at p such that its strict …

… Francisco Monserrat (Universitat Politècnica de València), The cone of curves and the
Cox ring of rational surfaces given by divisorial valuations. • Tomasz Szemberg (Pedagogical …

… Given a divisorial discrete valuation centered at infinity on C[x,y], we show that its sign on
C[… a given valuation centered at infinity and give a characterization of the divisorial valuations …