55 reputation
7
bio website math.utah.edu/~das
location Salt Lake City, Utah.
age 29
visits member for 2 years, 1 month
seen Sep 22 at 4:27
I am a Graduate Student at the University of Utah studying Birational Geometry.

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