Arithmetic and geometric deformations of -pure and -regular singularities
K Sato, S Takagi - arXiv preprint arXiv:2103.03721, 2021 - arxiv.org
… We also prove that two-dimensional strongly F-regular singularities are stable under equal
characteristic … First we observe that R is an N-graded Z-algebra with respect to the grading …
characteristic … First we observe that R is an N-graded Z-algebra with respect to the grading …
Global -regularity for weak del Pezzo surfaces
T Kawakami, H Tanaka - arXiv preprint arXiv:2404.04790, 2024 - arxiv.org
… Fano varieties play a significant role in the classification of … all the singularities of X are
strongly F-regular (see Lemma 3.9). … Given a normal variety X, we say that X is F-pure (resp. …
strongly F-regular (see Lemma 3.9). … Given a normal variety X, we say that X is F-pure (resp. …
Finite generation of split F-regular monoid algebras
R Datta, K Schwede, K Tucker - arXiv preprint arXiv:2402.16974, 2024 - arxiv.org
… F-regular rings form an important class of singularities in … Note that in the two-dimensional
case, one is just checking … On the other hand, if R is F-pure regular, then we only get purity of …
case, one is just checking … On the other hand, if R is F-pure regular, then we only get purity of …
Linearly reductive quotient singularities
… We classify lrq singularities in dimension 3 that are not … lrq singularities, which is why we
will simply write F-regular … Both cases occur: the two-dimensional rational double points …
will simply write F-regular … Both cases occur: the two-dimensional rational double points …
Steenbrink type vanishing for surfaces in positive characteristic
T Kawakami - arXiv preprint arXiv:2402.08153, 2024 - arxiv.org
… , B) if it is lc and p > 5, or it is F-pure. We also show that rational surface singularities satisfying
the vanishing are F-injective. … F-regular and F-pure rings vs. log terminal and log canonical …
the vanishing are F-injective. … F-regular and F-pure rings vs. log terminal and log canonical …
-rationality of two-dimensional graded rings with a rational singularity
K Shibata - arXiv preprint arXiv:2012.11090, 2020 - arxiv.org
… F-regular ring has log terminal singularities and an Fpure … of a two-dimensional graded
ring with a rational singularity in … In Section 5, we classify two-dimensional graded rings with a …
ring with a rational singularity in … In Section 5, we classify two-dimensional graded rings with a …
On Frobenius liftability of surface singularities
T Kawakami, T Takamatsu - arXiv preprint arXiv:2402.08152, 2024 - arxiv.org
… singularity (P ∈ X, B) is F-liftable if and only if it is F-pure and … classical F-singularities, such
as F-pure and strongly F-regular … freely use the classification of lc surface singularities [Kol13, …
as F-pure and strongly F-regular … freely use the classification of lc surface singularities [Kol13, …
F-signature functions of diagonal hypersurfaces
A Caminata, S Shideler, K Tucker, F Zerman - arXiv preprint arXiv …, 2024 - arxiv.org
… 38] and s(R) > 0 if and only if R is strongly F-regular [2]. On … with the line y = 1 gives the F-pure
threshold [4]. On the other … 3.5) or some1 two-dimensional ADE singularities (Remark 4.7). …
threshold [4]. On the other … 3.5) or some1 two-dimensional ADE singularities (Remark 4.7). …
Non-commutative resolutions of linearly reductive quotient singularities
… if R is not strongly F-regular, then it can be F-pure [25, Section … In this section, we study
two-dimensional LRQ singularities … a couple of classes of singularities, such as singularities on ℚ…
two-dimensional LRQ singularities … a couple of classes of singularities, such as singularities on ℚ…
F-thresholds cI (m) for projective curves
V Trivedi - Journal of Pure and Applied Algebra, 2022 - Elsevier
… We show that if R is a two dimensional standard graded domain … If R is strongly F-regular on
the punctured spectrum (for … canonical threshold in terms of F-pure thresholds (where fpt m ( …
the punctured spectrum (for … canonical threshold in terms of F-pure thresholds (where fpt m ( …