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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…
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…
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…
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…