34 citations · 46 across the 9 of their papers we have counts for
13 papers
Minkowski decompositions and universal equivariant deformations of toric pairs
Matej Filip
Let be the affine normal toric variety associated with a full-dimensional strongly convex rational polyhedral cone , and let be a primitive degree with slice $P_m=σ\ca…
Unobstructedness of affine Gorenstein terminal toric fourfolds
Matej Filip, Aljaž Zalar
We prove that every affine terminal Gorenstein toric variety of dimension at most four is unobstructed. In dimension four, the obstruction space need not vanish; instead, we determ…
Laurent polynomials and deformations of non-isolated Gorenstein toric sigularities
Matej Filip
We establish a correspondence between one-parameter deformations of an affine Gorenstein toric pair , defined by a polytope , and mutations of a Laurent pol…
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…
Smoothing toroidal crossing spaces
Simon Felten, Matej Filip, Helge Ruddat
We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very co…
A differential graded Lie algebra controlling the Poisson deformations of an affine Poisson variety
Matej Filip
We construct a differential graded Lie algebra $\fg$ controlling the Poisson deformations of an affine Poisson variety. We analyse $\fg$ in the case of affine Gorenstein toric Pois…
The Gerstenhaber product $\HH^2(A)\times \HH^2(A)\to \HH^3(A)$ of affine toric varieties
Matej Filip
For an affine toric variety $\spec(A)$, we give a convex geometric interpretation of the Gerstenhaber product $\HH^2(A)\times \HH^2(A)\to \HH^3(A)$ between the Hochschild cohomolog…
Hochschild Cohomology and Deformation Quantization of Affine Toric Varieties
Matej Filip
For an affine toric variety , we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Under certain assumptions we compute…
Rank two aCM bundles on the del Pezzo threefold of degree
Gianfranco Casnati, Matej Filip, Francesco Malaspina
We classify indecomposable aCM bundles of rank on the del Pezzo threefold of degree and analyze the corresponding moduli spaces.
Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds
Matej Filip
The aim of this paper is to classify indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on compete intersection Calabi-Yau (CICY) threefolds and prove the existence…