9 citations · 24 across the 15 of their papers we have counts for
17 papers
Polynomial factorization over henselian fields
Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +3
Given a valued field and an irreducible polynomial , we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading…
Valuations with infinite limit-depth
Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +1
For a certain field , we construct a valuation-algebraic valuation on the polynomial ring , whose Maclane--Vaquié chain consists of an infinite (countable) number of limit…
Irrational nef rays at the boundary of the Mori cone for very general blowups of the plane
Ciro Ciliberto, Rick Miranda, Joaquim Roé
In this paper we develop a technique for discovering (non-effective) irrational rays at the boundary of the Mori cone for linear systems on a general blowup of the plane, and give…
Okutsu frames of irreducible polynomials over henselian fields
Maria Alberich-Carramiñana, Jordi Guàrdia, Joaquím Roé +1
For a henselian valued field we establish a complete parallelism between the arithmetic properties of irreducible polynomials , encoded by their Okutsu frames, a…
Valuative trees over valued fields
Maria Alberich-Carramiñana, Jordi Guàrdia, Enric Nart +1
For an arbitrary valued field and a given extension of ordered groups, we analyze the structure of the tree formed by all -valued extensions of…
Newton-Okounkov bodies and Picard numbers on surfaces
Julio José Moyano-Fernández, Matthias Nickel, Joaquim Roé
We study the shapes of all Newton-Okounkov bodies of a given big divisor on a surface with respect to all rank 2 valuations of . We obtain upper bounds…