Embedded resolutions of non necessarily normal affine toric varieties

Resolutions for Equivariant Sheaves over Toric Varieties

In this work we construct global resolutions for general coherent equivariant sheaves over toric varieties. For this, we use the framework of sheaves over posets. We develop a notion of gluing of posets and of sheaves over posets, which we apply to construct global resolutions for equivariant sheaves. Our constructions give a natural correspondence between resolutions for reflexive equivariant ...

Embedded desingularization of toric varieties

We present a new method to achieve an embedded desingularization of a toric variety. Let W be a regular toric variety defined by a fan Σ and X ⊂ W be a toric embedding. We construct a finite sequence of combinatorial blowing-ups such that the final strict transforms X ′ ⊂ W ′ are regular and X ′ has normal crossing with the exceptional divisor.

Resolutions and Cohomologies of Toric Sheaves. The affine case

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of indecomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko states that the category of reflexive toric sheaves is equivalent to the category of vector spaces together with a certain family of filtrations. Within th...

Toric embedded resolutions of quasi-ordinary hypersurface singularities

We build two toric embedded resolutions procedures of a reduced quasiordinary hypersurface singularity (S, 0) of dimension d . The first one provides an embedded resolution as hypersurface of (C, 0) as a composition of toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection (S, 0) → (C, 0) . This gives a positive answer to a a question of Lipm...

Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties