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Mirror Symmetry and smoothing Gorenstein toric affine 3-folds
Alessio Corti, Matej Filip, Andrea Petracci
We state two conjectures that together allow one to describe the set of smoothing components of a Gorenstein toric affine 3-fold in terms of a combinatorially defined and easily st…
Deformations of an affine Gorenstein toric pair
Matej Filip
We consider deformations of a pair , where is an affine toric Gorenstein variety and is its boundary. We compute the tangent and obstruction space…
Versality in toric geometry
Klaus Altmann, Alexandru Constantinescu, Matej Filip
We study deformations of affine toric varieties. The entire deformation theory of these singularities is encoded by the so-called versal deformation. The main goal of our paper is…
Polyhedra, lattice structures, and extensions of semigroups
Klaus Altmann, Alexandru Constantinescu, Matej Filip
For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free…