Klaus Altmann

Strong Exceptional Sequences Provided by Quivers

Let Q be a finite quiver without oriented cycles. Denote by U → ℳ(Q) the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Extℳ(Q)l (U, U) = 0 for all l > 0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for when this algebra is isomorphic to the path algebra of the quiver Q. If so, then the bounded derived categories of finitely generated right k Q-modules and that of coherent sheaves on ℳ(Q) are related via the full and faithful functor − ⊗kQL U.

THE GEOMETRY OF T-VARIETIES

This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity theory and the theory of hyperbolic algebraic varieties.We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.We introduce a variety

Infinitesimal deformations and obstructions for toric singularities

\hat{G}_2

Explicit Birational Geometry of 3-Folds: One parameter families containing three dimensional toric Gorenstein singularities

parameterizing isotropic five-spaces of a general degenerate four-form in a seven dimensional vector space. It is in a natural way a degeneration of the variety

P-Resolutions of Cyclic Quotients from the Toric Viewpoint

G_2

Computation of the vector space T1 for affine toric varieties

, the adjoint variety of the simple Lie group

Torsion of differentials on toric varieties

\mathbb{G}_2

Negative Deformations of Toric Singularities that are Smooth in Codimension Two

. It occurs that it is also the image of

Flow polytopes and the graph of reflexive polytopes

\mathbb{P}^5

A Vanishing Result for the Universal Bundle on a Toric Quiver Variety

by a system of quadrics containing a twisted cubic. Degenerations of this twisted cubic to three lines give rise to degenerations of