Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Roé, Joaquim"'
We show the existence of cones over 8-dimensional rational spheres at the boundary of the Mori cone of the blow-up of the plane at $s\geq 13$ very general points. This gives evidence for De Fernex's strong $\Delta$-conjecture, which is known to imply
Externí odkaz:
http://arxiv.org/abs/2310.10507
Autor:
Alberich-Carramiñana, Maria, Guàrdia, Jordi, Nart, Enric, Poteaux, Adrien, Roé, Joaquim, Weimann, Martin
Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaqui\'e and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the factorization
Externí odkaz:
http://arxiv.org/abs/2207.02139
For a certain field $K$, we construct a valuation-algebraic valuation on the polynomial ring $K[x]$, whose Maclane--Vaqui\'e chain consists of an infinite (countable) number of limit augmentations
Comment: arXiv admin note: substantial text over
Comment: arXiv admin note: substantial text over
Externí odkaz:
http://arxiv.org/abs/2204.03365
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 examples of such irrational rays.
Comment: 14 pages. Comments wel
Comment: 14 pages. Comments wel
Externí odkaz:
http://arxiv.org/abs/2201.08634
For a henselian valued field $(K,v)$ we establish a complete parallelism between the arithmetic properties of irreducible polynomials $F\in K[x]$, encoded by their Okutsu frames, and the valuation-theoretic properties of their induced valuations $v_F
Externí odkaz:
http://arxiv.org/abs/2111.02811
For an arbitrary valued field $(K,v)$ and a given extension $v(K^*)\hookrightarrow\Lambda$ of ordered groups, we analyze the structure of the tree formed by all $\Lambda$-valued extensions of $v$ to the polynomial ring $K[x]$. As an application, we f
Externí odkaz:
http://arxiv.org/abs/2107.09813
We study the shapes of all Newton-Okounkov bodies $\Delta_{v}(D)$ of a given big divisor $D$ on a surface $S$ with respect to all rank 2 valuations $v$ of $K(S)$. We obtain upper bounds for, and in many cases we determine exactly, the possible number
Externí odkaz:
http://arxiv.org/abs/2101.05338
Autor:
Alberich-Carramiñana, Maria, Boix, Alberto F., Fernández, Julio, Guàrdia, Jordi, Nart, Enric, Roé, Joaquim
Let $\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with coefficients in a field $K$. We prove comparison theorems between MacLane-Vaqui\'e key polynomials for valuations $\mu\le\nu$ and abstract key polynomials for $\nu$. Also,
Externí odkaz:
http://arxiv.org/abs/2005.04406
Autor:
Roé, Joaquim, Szemberg, Tomasz
The Newton--Okounkov body of a big divisor D on a smooth surface is a numerical invariant in the form of a convex polygon. We study the geometric significance of the shape of Newton--Okounkov polygons of ample divisors, showing that they share severa
Externí odkaz:
http://arxiv.org/abs/1911.09708
We show that the subgraph of the concave transform of a multiplicative filtration on a section ring is the Newton--Okounkov body of a certain semigroup, and if the filtration is induced by a divisorial valuation, then the associated graded algebra is
Externí odkaz:
http://arxiv.org/abs/1901.00384