Search results for "Birational geometry"
showing 4 items of 4 documents
Automorphisms of $mathbb{A}^{1}$-fibered affine surfaces
2011
We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface S of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of S is generated by automorphisms preserving these fibrations.
Cluster tilting for one-dimensional hypersurface singularities
2008
In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite dimensional symmetric and satisfy $\tau^2=\id$. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities.
Actions de tores algébriques sur des corps de caractéristique zéro
2023
Over an algebraically closed field of characteristic zero, normal affine varieties endowed with an effective torus action were described by Altmann and Hausen in 2006 by a geometrico-combinatorial presentation.Using Galois descent tools, we extend this presentation to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may be non split and may have non-trivial torsors, thus we need additional data to encode such varieties. We provide some situations where the generalized Altmann-Hausen presentation simplifies. For instance, if the acting torus is split, we recover mutatis mutandis the original Altmann-Hausen presentation. Finally, …
On the birational geometry of the universal Picard variety
2010
We compute the Kodaira dimension of the universal Picard variety P_{d,g} parameterizing line bundles of degree d on curves of genus g under the assumption that (d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we investigate for which degrees the universal Picard varieties are birational.