6 citations · 21 across the 13 of their papers we have counts for
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Linear maps in minimal free resolutions of Stanley-Reisner rings
Lukas Katthän
In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex . Indeed, the differenti…
The Symmetric signature of cyclic quotient singularities
Alessio Caminata, Lukas Katthän
The symmetric signature is an invariant of local domains which was recently introduced by Brenner and the first author in an attempt to find a replacement for the -signature in…
A non-Golod ring with a trivial product on its Koszul homology
Lukas Katthän
We present a monomial ideal such that is not Golod, even though the product on its Koszul homology is trivial. This constitutes a countere…
A Canonical module characterization of Serre's
Lukas Katthän, Kohji Yanagawa
In this short note, we give a characterization of domains satisfying Serre's condition in terms of their canonical modules. In the special case of toric rings, thi…
The Golod property for Stanley-Reisner rings in varying characteristic
Lukas Katthän
We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set of prime numbers we construct…
Stanley depth and simplicial spanning trees
Lukas Katthän
We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection…
Two lower bounds for the Stanley depth of monomial ideals
Lukas Katthän, Seyed Amin Seyed Fakhari
Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On t…
Non-normal affine monoids
Lukas Katthän
We give a geometric description of the set of holes in a non-normal affine monoid . The set of holes turns out to be related to the non-trivial graded components of the local co…