bio  website  front.math.ucdavis.edu/… 

location  Cornell  
age  44  
visits  member for  4 years, 6 months 
seen  8 hours ago  
stats  profile views  9,141 
Math professor at Cornell,
PhD 1996
20h

comment 
Does normalization of projective varieties preserve very ampleness
I don't understand the two comments above. Take $\mathcal O(1)$ on $\mathbb P^2$ and restrict to a nodal cubic $X$. Then $f^* L$ is degree $3$ on $\tilde X$, hence very ample, no? 
Apr 15 
revised 
The moduli space of special Lagrangian submanifolds
edited body 
Apr 15 
revised 
Error term in formula for products of necklaces
edited title 
Apr 12 
comment 
Is the big cell a principal open set?
This is missing perhaps the most concrete and interesting part, which is what the function is. The answer is $g \mapsto \prod_\omega \langle \vec v^\omega, g \cdot \vec v_\omega \rangle$ where $\omega$ ranges over the fundamental representations. The property you want of $G$ is that you have all these fundamental representations available. Note that this function generalizes the one you mentioned for $GL(n)$. 
Apr 8 
comment 
Cotangent bundle of coadjoint orbit is stein manifold?
To spell out the connection between the spaces more tightly: consider the map $(G \times \mathfrak{b})/B \to \mathfrak g$, $[g,X] \mapsto g\cdot X$, where $B$ acts on the right of $G$ and by conjugation on $\mathfrak b$. Then map further to $\mathfrak g/G = \mathfrak t/W$. The fibers of this flat map are $T^* G/B$ over $0$ and $G/T$ over a general point. 
Mar 25 
comment 
What is the combinatorial data classifying nonnormal affine toric varieties?
There's even a game exploiting this difficulty: en.wikipedia.org/wiki/Sylver_coinage 
Mar 25 
comment 
Relation between intersection multiplicity and HilbertSamuel multiplicities
In $e_P(X) e_P(Y) e_P(X)$, should the third term be $e_P(Z)$? And if $K$ is infinite, what happens if you look instead at a point in $V \cap P$ where $V$ is a generic $3$plane? 
Mar 22 
awarded  Announcer 
Mar 22 
comment 
What is the definition of “canonical”?
I'm surprised that noone has complained about the term "canonical bundle" in algebraic geometry, meaning the top exterior power of the cotangent bundle. Let me do so here. 
Mar 22 
comment 
Existence of parametrizations of rational orthogonal matrices
Once you've parametrized an open set on an algebraic group, cover the group with finitely many left translates, to get everything. Which is what's done in the reference above, where the translates are by diagonal matrices with entries $\pm 1$. Also: Kostant and Michor have a Cayley transform for other semisimple groups. (In the split case you can use the Bruhat decomposition.) 
Mar 22 
comment 
About structure of parabolic subgroups of finite classical algebraic groups
Let me spell out a framework I think is useful here. Given a set $S$ of simple roots (which will be the ones not in your parabolic), define the $S$height of a root $\beta$ to be the sum of the coefficients on $S$, when expanding $\beta$ in simple roots. Let $m$ be the maximum $S$height. Then for each $k\in [0,m]$ we can define a normal subgroup $J_k$ of $P$, using those roots of height $\geq k$, and $P = J_0 > J_1 > \ldots > J_m$. (Also $J_1 = Rad(P)$.) For your question, you want $m=1$. For $P$ maximal, $m$ is the coefficient of $P$'s missing simple root in the highest root. 
Mar 22 
comment 
Zariski closure of orbits of real groups on complex flag manifolds
Thanks! I will ponder this version of the question. 
Mar 20 
revised 
Weyl group action on complexified Iwasawa decomposition
added 115 characters in body 
Mar 20 
answered  Weyl group action on complexified Iwasawa decomposition 
Mar 20 
revised 
The amplituhedron minus the physics
added 707 characters in body 
Mar 20 
revised 
The amplituhedron minus the physics
deleted 88 characters in body 
Mar 20 
comment 
The amplituhedron minus the physics
While quite readable, they do make the two points I'm complaining about above rather difficult! I will edit. 
Mar 19 
comment 
The amplituhedron minus the physics
Also, there's no orthogonality involved in defining the $G(2,m)$ bundles; rather, they live in the quotient space. (In ordinary algebraic geometry over a field this would be a distinction without a difference. But here it's very difficult to understand positivity when involving an inner product, and we don't have to.) 
Mar 19 
comment 
The amplituhedron minus the physics
I found the reference to the map $Y_{n,k,m}$, as taking two inputs, very confusing. $Z$ is fixed and one should take $Y_{n,k,m}$ as a function from $G_+(k,n)$. Also, the amplituhedron as a space is not what's interesting, but as a space plus meromorphic volume form. The positivereal structure is there to help nail down this form; it is supposed to have no poles on the interior of the amplituhedron. 
Mar 18 
comment 
Zariski closure of orbits of real groups on complex flag manifolds
I'm having trouble unpacking your description. What are the complex points of the space you suggest I find containing $G_{\mathbb C}/B_{\mathbb C}$ as the $\mathbb R$points? 