# On rational surfaces, II

@inproceedings{Nagata1960OnRS,
title={On rational surfaces, II},
author={M. Nagata},
year={1960}
}
247 Citations
On (-1) classes
• Mathematics
• 2019
In this paper we study (-1) classes} for the blow up of n-dimensional projective space in several points. We generalize Noether's inequality, and we prove that all (-1) classes are in bijectiveExpand
Explicit Brill-Noether-Petri general curves
• Mathematics
• 2015
Let $p_1,\dots, p_9$ be the points in $\mathbb A^2(\mathbb Q)\subset \mathbb P^2(\mathbb Q)$ with coordinates (-2,3),(-1,-4),(2,5),(4,9),(52,375), (5234, 37866),(8, -23), (43, 282),Expand
Inverse systems, Gelfand-Tsetlin patterns and the weak Lefschetz property
• Mathematics, Computer Science
• J. Lond. Math. Soc.
• 2011
The inverse system dictionary is used to connect I to an ideal of fat points and it is shown that failure of WLP for powers of linear forms is connected to the geometry of the associated fat point scheme. Expand
Geometric Aspects of Polynomial Interpolation in More Variables and of Waring’s Problem
In this paper I treat the problem of determining the dimension of the vector space of homogeneous polynomials in a given number of variables vanishing with some of their derivatives at a finite setExpand
Deformations of algebraic varieties with G[m] action
© Société mathématique de France, 1974, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec lesExpand
Comparing powers and symbolic powers of ideals
• Mathematics
• 2007
We develop tools to study the problem of containment of symbolic powers $I^{(m)}$ in powers $I^r$ for a homogeneous ideal $I$ in a polynomial ring $k[{\bf P}^N]$ in $N+1$ variables over anExpand
Rational surfaces having only a finite number of exceptional curves
Abstract.We characterize the rational surfaces X which have a finite number of (-1)-curves under the assumption that -KX is nef and having self-intersection zero.
Birational classification of curves on rational surfaces
• Mathematics
• Nagoya Mathematical Journal
• 2010
Abstract In this paper we consider the birational classification of pairs (S, ℒ), with S a rational surface and ℒ a linear system on S. We give a classification theorem for such pairs, and weExpand
The third smallest Salem number in automorphisms of K3 surfaces
We realize the logarithm of the third smallest known Salem number as the topological entropy of a K3 surface automorphism with a Siegel disk and a pointwisely fixed curve at the same time. We alsoExpand
Homogeneous interpolation on ten points
• Mathematics
• 2008
In this paper we prove that for all pairs (d, m )w ithd/m ≥ 174/55, the linear system of plane curves of degree d with ten general base points of multiplicity m has the expected dimension.