7 papers
Obstructions to embedding singular curves in toric varieties
Maya Banks, Izzet Coskun, Kevin Tucker
For every integer , we show that there exists an irreducible, reduced curve which embeds in but in no projective normal toric variety of dimension less tha…
On rational chain connectedness of globally +-regular varieties
Emre Alp Özavcı, Zsolt Patakfalvi, Kevin Tucker +2
We prove that globally -regular varieties are rationally chain connected in dimension three and mixed characteristic with residue field characteristic . We also introduce a…
-intersection flatness of dagger and Berkovich Tate algebras
Rankeya Datta, Jack J Garzella, Kevin Tucker
We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic h…
Limit -signature functions of two-variable binomial hypersurfaces
Anna Brosowsky, Izzet Coskun, Suchitra Pande +1
The -signature is a fundamental numerical invariant of singularities in positive characteristic. Its positivity detects strong -regularity, an important class of singularitie…
Variants on Frobenius Intersection Flatness and Applications to Tate Algebras
Rankeya Datta, Neil Epstein, Karl Schwede +1
The theory of singularities defined by Frobenius has been extensively developed for -finite rings and for rings that are essentially of finite type over excellent local rings. H…
F-Splittings of seminormal monoid algebras
Milena Hering, Kevin Tucker
We compute a number of invariants of singularities defined via the Frobenius morphism for seminormal affine toric varieties over fields of characteristic p > 0. Our main technical…
F-signature functions of diagonal hypersurfaces
Alessio Caminata, Samuel Shideler, Kevin Tucker +1
Let be a diagonal hypersurface in . We study the behavior of the function $ϕ_{f,p}({a}/{p^e})=p^{-ne}\dim_{\mathbb{F}_p}\big(A_p/(x_1^{p^e},\…