Optimal bounds on surfaces
J Liu, VV Shokurov - arXiv preprint arXiv:2305.19248, 2023 - arxiv.org
We prove that the first gap of $\mathbb R $-complementary thresholds of surfaces is $\frac
{1}{13} $. More precisely, the largest $\mathbb R $-complementary threshold for surfaces …
{1}{13} $. More precisely, the largest $\mathbb R $-complementary threshold for surfaces …
Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic
T Kawakami - Advances in Mathematics, 2022 - Elsevier
We show that the Bogomolov-Sommese vanishing theorem holds for a log canonical
projective surface (X, B) in large characteristic unless the Iitaka dimension of K X+⌊ B⌋ is …
projective surface (X, B) in large characteristic unless the Iitaka dimension of K X+⌊ B⌋ is …
On Frobenius liftability of surface singularities
T Kawakami, T Takamatsu - arXiv preprint arXiv:2402.08152, 2024 - arxiv.org
We show that a plt surface singularity $(P\in X, B) $ is $ F $-liftable if and only if it is $ F $-
pure and is not a rational double point of type $ E_8^ 1$ in characteristic $ p= 5$. As a …
pure and is not a rational double point of type $ E_8^ 1$ in characteristic $ p= 5$. As a …
Steenbrink type vanishing for surfaces in positive characteristic
T Kawakami - arXiv preprint arXiv:2402.08153, 2024 - arxiv.org
Let $(X, B) $ be a pair of a normal surface over a perfect field of characteristic $ p> 0$ and
an effective $\mathbb {Q} $-divisor $ B $ on $ X $. We prove that Steenbrink type vanishing …
an effective $\mathbb {Q} $-divisor $ B $ on $ X $. We prove that Steenbrink type vanishing …
On local rings without small Cohen-Macaulay algebras in mixed characteristic
K Shimomoto, E Tavanfar - arXiv preprint arXiv:2109.12700, 2021 - arxiv.org
For any $ d\ge 4$, by deformation theory of schemes, we present examples of (complete or
excellent) $ d $-dimensional mixed characteristic normal local domains admitting no small …
excellent) $ d $-dimensional mixed characteristic normal local domains admitting no small …
On the Kawamata-Viehweg vanishing theorem for log Calabi-Yau surfaces in large characteristic
T Kawakami - arXiv preprint arXiv:2211.08751, 2022 - arxiv.org
arXiv:2211.08751v2 [math.AG] 25 Oct 2023 Page 1 arXiv:2211.08751v2 [math.AG] 25 Oct 2023
ON THE KAWAMATA-VIEHWEG VANISHING THEOREM FOR LOG CALABI-YAU SURFACES …
ON THE KAWAMATA-VIEHWEG VANISHING THEOREM FOR LOG CALABI-YAU SURFACES …