arXiv subjects

Witold Kraśkiewicz

Publications and source records attributed to Witold Kraśkiewicz.

3 recordsLinked to original sources

arXiv2019

Geometry of orbit closures for the representations associated to gradings of Lie algebras of types $E_6$, $F_4$ and $G_2$

In this paper we investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on a simple Lie algebras of type $E_6$, $F_4$ and $G_2$. The methods for classifying the orbits for these actions were developed by Vinberg. We give the orbit descriptions, the degeneration partial orders, and decide the normality of the orbit closures. We also investigate the rational singularities, Cohen-Macaulay and Gorenstein properties for the orbit closures. We give the generators of the defining ideals of orbit closures.

math.RT↗

arXiv2018

The family of perfect ideals of codimension 3, of type 2 with 5 generators

In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. This family is likely to play a key role in classifying perfect ideals with five generators of type two.

math.AC↗

arXiv2011

Generic decompositions and semi-invariants for string algebras

We investigate the rings of semi-invariants for tame string algebras A(n) of non-polynomial growth. We are interested in dimension vectors of band modules. We use geometric technique related to the description of coordinate rings on varieties of complexes. The fascinating combinatorics emerges, showing that our rings of invariants are the rings of some toric varieties. We show that for $n\le 6$ the rings of semi-invariants are complete intersections but we show an example for $n=7$ that this is not the case in general.

math.RT↗