arXiv subjects

Dennis Keeler

Publications and source records attributed to Dennis Keeler.

3 recordsLinked to original sources

arXiv2026

Normal extensions of twisted graded Calabi--Yau algebras

We discuss three families of twisted graded Calabi--Yau algebras of dimension three that arise through the process of normal extensions. In addition to the twisted Calabi--Yau condition, we prove that these algebras are noetherian piecewise domains under a non-degeneracy condition. We show that these algebras can also be constructed as certain iterated skew polynomial rings. Finally, we discuss how these algebras shed light on possible types of twisted graded Calabi--Yau algebras of dimension four.

math.RA↗

arXiv2026

Quiver down-up algebras of type A

We present a generalization of down-up algebras, originally defined by Benkart and Roby. These quiver down-up algebras arise as quotients of the double of the extended Dynkin quiver of type A. Under a certain non-degeneracy condition, we show that quiver down-up algebras are noetherian piecewise domains, and that they are twisted Calabi--Yau. Finally, we consider the isomorphism problem for graded quiver down-up algebras.

math.RA↗

arXiv2018

Arithmetically nef line bundles

Let $L$ be a line bundle on a scheme $X$, proper over a field. The property of $L$ being nef can sometimes be "thickened", allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line bundle $L$ may be nef, but not arithmetically nef. We show that $L$ is arithmetically nef if and only if its restriction to its stable base locus is arithmetically nef. Consequently, if $L$ is nef and its stable base locus has dimension $1$ or less, then $L$ is arithmetically nef.

math.AG↗