12,982 reputation
22255
bio website personal.psu.edu/kes32
location Pennsylvania
age 35
visits member for 4 years, 7 months
seen 1 hour ago

I'm an assistant professor at Penn State. I work on algebraic geometry and commutative algebra.


1h
comment How to check if a symmetric random variables is the difference of two iid symmetric random variables
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16h
reviewed Close Where to find (personal) motivation
19h
comment Does the canonical morphism commute with the inverse image functor?
This certainly looks commutative to me. Chasing a global section of $F(n)$ (over a chart of $S$) around seems ok (is there some subtlety I'm missing?). Also, in the first displayed equation, shouldn't that be $\Phi^* F(n)$ not $\phi^* F(n)$?
1d
reviewed Leave Open Automorphism group of a smooth quadric $Q\subset\mathbb{P}^4$
2d
reviewed Close Expected value when rolling multiple k-sided dice and keeping the highest score and 1s cancelling higest remaining values
Aug
18
reviewed Leave Open Linear dependency of real numbers with integer coefficients adding up to zero
Aug
17
reviewed Leave Open Are there two non-homotopy equivalent spaces with equal homotopy groups?
Aug
17
reviewed Leave Open How short can we state the Axiom of Choice?
Aug
15
reviewed Leave Open Star shaped sets with a midpoint
Aug
15
reviewed Leave Open What is parameterization of the trefoil knot surface in R³?
Aug
14
reviewed Close graph and tree problems helps
Aug
14
reviewed No Action Needed Why is the mirror of resolved conifold the deformed conifold?
Aug
14
reviewed Close Find out acceptance rate / selectiveness of conference
Aug
13
reviewed Close Factoring a semiprime is easier than matrix multiplication?
Aug
13
reviewed Leave Open Natural candidates for 'hyperplanes' in biprojective spaces
Aug
13
comment Which singularities of log pairs do not depend on the resolution?
Hi, the problem is that for canonical or terminal, you exclude certain divisors, the nonexceptional divisors. As you blowup, more and more valuations become nonexceptional. In particular, if you start with the example I gave you on $\mathbb{A}^2$, the lines have discrepancy $-1 + \varepsilon < 0$. But this doesn't stop things from being canonical since they are non-exceptional. The blowup at the origin shows it isn't canonical. On the other hand, for every KLT $(X, \Delta)$ there is a log resolution $Y \to X$ with $(Y, \Delta_Y = -K_Y + \pi^*(K_X + \Delta))$ having canonical singularities.
Aug
12
reviewed Leave Open Chow group of zero-cycles generated by open dense subscheme
Aug
12
comment Which singularities of log pairs do not depend on the resolution?
Dear Li Yutong, I don't have Kollár-Mori in front of me, what's the idea of 2.30? The reason that KLT/LC are ok is because there is no distinction between exceptional and non-exceptional discrepancies (note the discrepancy of a non-exceptional divisor is just the coefficient of $\Delta$ along it). In particular, what is exceptional over $X$ is not always exceptional over $Y$.
Aug
11
revised Which singularities of log pairs do not depend on the resolution?
added 365 characters in body
Aug
11
revised Which singularities of log pairs do not depend on the resolution?
clarified a point