#### 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 bijective… Expand

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

- Mathematics
- 2001

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 set… Expand

Deformations of algebraic varieties with G[m] action

- Mathematics
- 1974

© 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 les… Expand

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 an… Expand

Rational surfaces having only a finite number of exceptional curves

- Mathematics
- 2004

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 we… Expand

The third smallest Salem number in automorphisms of K3 surfaces

- Mathematics
- 2009

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 also… Expand

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.