bio | website | front.math.ucdavis.edu/… |
---|---|---|
location | Cornell | |
age | 45 | |
visits | member for | 5 years, 9 months |
seen | Jul 23 at 0:03 | |
stats | profile views | 11,307 |
Math professor at Cornell,
PhD 1996
Jul 24 |
awarded | Popular Question |
Jul 20 |
awarded | Nice Answer |
Jul 18 |
awarded | Nice Answer |
Jul 9 |
revised |
Is there a tropical geometric proof for counting genus g curves in any n dimensional projective space?
Fixed Soibelman |
Jul 6 |
comment |
Orientation form on the blow up of a Kaehler manifold
I agree that in that example you could pick the form you said. What my example shows is that if you pick a random form and then scale it to be good for $X$, it may not work for $Y$. So if you want it for both (which I'm not convinced you really do -- but it's what you wrote), you need a real argument. |
Jul 4 |
comment |
Orientation form on the blow up of a Kaehler manifold
I don't see how you can normalize the integral to be 1 on $X$ and $Y$ simultaneously. For example, take $X$ to be the product of two $\mathbb P^1$s with areas $r, 1/r$, and $Y = \mathbb P^1 \times pt$. |
Jun 30 |
comment |
Smooth morphism to homogeneous spaces and fibers
I usually use "$f$ is equivariant". |
Jun 30 |
comment |
Picard group of a quotient of a group by its maximal parabolic subgroup
You can't say "the" maximal parabolic; there's usually more than one, even up to conjugacy. But for every such $P$ this is true. |
Jun 30 |
answered | Shared maximum eigenvector |
Jun 28 |
revised |
What is deforming this non-complete intersection like?
made title more specific to the question |
Jun 28 |
reviewed | Approve What is deforming this non-complete intersection like? |
Jun 26 |
awarded | Nice Question |
Jun 26 |
comment |
Number of $\mathbb F_p$ points constant mod $p$?
Your #4 sounds like "what does it imply?" rather than "what does it suggest?" (what would imply it, that one should be on the lookout for?). I have a certain class of varieties; I don't know what properties they have, but now I'm going to try to prove rational connectivity directly for them (not actually imply it from the point-counting fact). |
Jun 26 |
comment |
Number of $\mathbb F_p$ points constant mod $p$?
I'd certainly like to compute $\#X(\bf F_p)$ but don't expect to have much luck. |
Jun 25 |
asked | Number of $\mathbb F_p$ points constant mod $p$? |
Jun 21 |
comment |
A homeomorphism between total spaces with same fiber and base spaces not homotopic
Or more generally, if $F\to E\to B$ is a bundle with $E$ not a product, then $F\times E \to E$, $F\times E \to F\times B$ works. |
Jun 18 |
comment |
Combinatorial results by Poincaré duality
If you're willing to extend this from "Poincar\'e duality" to "properties of Betti numbers", then you could include Hard Lefschetz in your toolset, and get Stanley's proof of the Upper Bound Theorem for the number of faces of a simplicial polytope. |
Jun 17 |
comment |
How to embed $U(1)$ into a bigger group, using Dynkin diagrams
The "remove the top root" step amounts to "take the centralizer in $E_7$ of a certain element of adjoint order $2$". Look around MO for Borel-de Siebenthal theory, which is about subgroups of the same rank as the big group. |
Jun 16 |
comment |
q-Catalan numbers from Grassmannians
Hard Lefschetz tells you that the even Betti numbers have to increase to the middle, then decrease (they're "unimodal"). |
Jun 13 |
comment |
How to prove this polynomial always has integer values at all integers?
I really don't know how to connect $\mathbb Z$-valuedness and evenness. If $x^2=y$ so we can rewrite $P(x)$ as $P(y)$, then $P$ being $\mathbb Z$-valued at all $y\in\mathbb Z$ is (much?) stronger than its being $\mathbb Z$-valued at all $x\in\mathbb Z$. Do your computed polynomials have $\mathbb Z$-coefficients expanded in $\{ {y \choose k} \}$? |