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Jul
2 |
awarded | Curious |
Mar
5 |
asked | How to Calculate Minimal Log Discrepancy on a Toric Variety? |
Aug
17 |
comment |
On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier
Thanks again, I will look at those papers. |
Aug
17 |
accepted | On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier |
Aug
17 |
comment |
On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier
Thank you very much Karl. One last question, is there anyway to define Sharp F-purity or Strongly F-regular for this kind of pairs ? |
Aug
16 |
revised |
On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier
deleted 14 characters in body |
Aug
16 |
asked | On Non F-pure ideal and Sharp F-Purity for a pair $(X, \Delta)$ where $K_X+\Delta$ is NOT $\mathbb{Q}$-Cartier |
Apr
21 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Thanks Laurent! |
Apr
20 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Got it! Thanks again. |
Apr
20 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Thanks Angelo, could you please give a proof of this fact or probably suggest a reference? |
Apr
20 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Hi Laurent, You are right, $S$ does bot have any ''natural'' $k(x)$-scheme structure but there is a obvious ''non natural'' $k(x)$-scheme structure, since I started with a Variety $X$, so $k(x)\hookrightarrow \mathcal{O}_{X,\ x}$ and the only reason for doing this is to get a finite type morphism so that I can say $S$ is a variety. Now that you asked about it, I am little worried, is $\mathcal{O}_{X,\ x}$ a finitely generated $k(x)$ algebra ? I always thought it is, but now I am not so sure! |
Apr
20 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Hi Karl and Angelo, thanks for taking time to read my problem. Here is exactly what I have and what I need. Let $X$ be a normal variety over an algebraically closed filed $k$ of char $p>0$. Let $x$ be codim $2$ point of $X$. Assume $S=\text{Spec }\mathcal{O}_{X,\ x}$. Then $S$ is a surface over the field $k(x)$. Now by Lipman, $S$ has a resolution of singularities, call $f:Y\to S$. Let $B$ be a $\mathbb{Q}$-Cartier $\mathbb{Q}$ divisor such that $B$ is $f$-nef and $f$-big and the fractional part of $B$ has SNC support. Then $R^if_*\mathcal{O}_X(K_Y+\lceil B\rceil)=0$ for all $i>0$. |
Apr
19 |
comment |
Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces
Yes Angelo you are right, Kadaira vanishing does fail in char positive even on a surface, but some version of Kawamata-Viehweg vanishing theorem which is sufficient to the run the Minimal Model Program continues to hold even in positive characteristic for surfaces. You can look for a reference in the paper I mentioned above or in a preprint by Kollar and Kovacs, "Birational Geometry of Log Surfaces" |
Apr
19 |
asked | Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces |
Apr
17 |
revised |
Adjunction Formula for Weil Divisors on a Normal Variety X
Corrected spelling |
Apr
17 |
comment |
Adjunction Formula for Weil Divisors on a Normal Variety X
That is just a typo! I mean Divisor, sorry about that! |
Apr
17 |
revised |
Adjunction Formula for Weil Divisors on a Normal Variety X
deleted 157 characters in body |
Apr
17 |
revised |
Adjunction Formula for Weil Divisors on a Normal Variety X
Improved the description of the problem.; edited body |
Apr
17 |
asked | Adjunction Formula for Weil Divisors on a Normal Variety X |
Mar
27 |
awarded | Commentator |