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Journals and Conferences
In this paper we prove a conjecture about the dimension of linear systems of surfaces of degree d in P through at most eight multiple points in general position.
In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.
Different choices of basis yield (non-canonically) isomorphic Cox rings and any of them is a “total” coordinate ring for X in the sense that, (1) The homogeneous coordinate rings ⊕∞ s=0H (X, sD) of all images of X via complete linear systems φD : X → P(H(X,D)) are subalgebras of Cox(X). (2) If the Cox ring is a finitely generated k-algebra then X can be… (More)
We study Cox rings of K3-surfaces. A first result is that a K3surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3-surfaces of Picard number two, and explicitly compute the Cox rings of generic K3-surfaces with a non-symplectic… (More)
In this paper we introduce a technique to degenerate K3 surfaces and linear systems through fat points in general position on K3 surfaces. Using this degeneration we show that on generic K3 surfaces it is enough to prove that linear systems with one fat point are non-special in order to obtain the non-speciality of homogeneous linear systems through n = 49… (More)
In this paper we deal with linear systems of P3 through fat points. We consider the behavior of these systems under a cubic Cremona transformation that allows us to produce a class of special systems which we conjecture to be the only ones.
We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated.
Consider a (non-empty) linear system of surfaces of degree d in P through at most 8 multiple points in general position and let L denote the corresponding complete linear system on the blowing-up X of P along those general points. Then we determine the base locus of such linear systems L on X.
In this paper we prove the equivalence of two conjectures on linear systems through fat points on a generic K3 surface. The first conjecture is exactly as Segre conjecture on the projective plane. Whereas the second characterizes such linear system and can be compared to the Gimigliano-HarbourneHirschowitz conjecture.