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5 papers · 2 filters
Maximal variation of linear systems
Arnaud Beauville
Let X be a smooth projective complex variety, and L a line bundle on X . We say that the linear system |L| has maximal variation if its elements have the maximum number dim|L| of m…
Mumford-type Shimura curves contained in the Torelli locus
Thomas Bouchet, Jeroen Hanselman, Andreas Pieper +1
In this article we give explicit equations for two Shimura families of genus 4 curves whose Jacobians are abelian fourfolds of Mumford type. These are the first explicit examples o…
Płoski Approximation Theorem
Adam Parusiński, Guillaume Rond
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example o…
Free line arrangements with low maximal multiplicity
Alexandru Dimca, Lukas Kühne, Piotr Pokora
Let $\A$ be a free arrangement of lines in the complex projective plane, with exponents . Let be the maximal multiplicity of points in $\A$. In this note, we d…
Hyperplane sections of cubic threefolds
Arnaud Beauville
Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .