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23098
bio website front.math.ucdavis.edu/…
location Cornell
age 45
visits member for 5 years, 5 months
seen 2 hours ago
Math professor at Cornell, PhD 1996

1h
comment Picard group of Schubert varieties
Indeed; one way to think about it is that we know the map $c_1:Pic\to H^2$ is an isomorphism for $G/B$, and this restriction fact says that the same is true for $X_w$. Since $X_w$ is a union of $G/B$'s cells it's easy to compute the map $H^2(G/B) \to H^2(X_w)$ and it has the kernel you describe.
13h
revised Root in positive Weyl chamber
added 68 characters in body
15h
answered Root in positive Weyl chamber
2d
answered Are there any Algebraic Geometry Theorems that were proved using Combinatorics?
Mar
26
answered Moduli space of flat connections over a torus
Mar
25
answered Continuity of Intersection Multiplicities
Mar
24
comment On Q-Cartier Divisors
I think the basic issue is that the notion of Cartier divisor is a scheme-theoretic one, and the notion of Weil divisor isn't, really. For example, consider the two pure codim 1 subschemes of $\{(x,y):xy=0\}$ defined by $x=y^2=0$ vs. $x^2=y=0$. Do you want those to be equal as Weil divisors (2x the origin)? I would say yes.
Mar
21
comment Derivation of Blattner's conjecture in the Beilinson-Bernstein picture
It's definitely got some of the ingredients, and in particular, draws attention to the importance of K-orbits with smooth closure. It doesn't reference Blattner directly though. Thanks!
Mar
21
comment Grobner basis and subsets
I agree; if $A$ is given as a finite list it's clear, otherwise it depends strongly on how $A$ is specified.
Mar
19
comment Geometric proof of Borel-Weil theorem
You might like Bott's short survey "On induced representations" in The mathematical heritage of Hermann Weyl (Durham, NC, 1987), 1–13, Proc. Sympos. Pure Math., 48, Amer. Math. Soc., Providence, RI, 1988. Personally, I find it a lot easier to use complex algebraic geometry to think about Borel-Weil (much less Borel-Weil-Bott!) but to each his own.
Mar
19
comment Richardson varieties over finite fields
Indeed it doesn't make a big difference: for each open Richardson in $X^\circ_w \cap X^v_\circ \subseteq G/P$, the open Richardson $X^\circ_w \cap X^v_\circ \subseteq G/B$ maps to it isomorphically, if $w,v \in W^P$ i.e. are minimal coset representatives in $W/W_P$.
Mar
19
revised Explicit equations for Schubert varieties
added 61 characters in body
Mar
19
asked Is the upper boundary of a Schubert variety Cartier?
Mar
11
revised The action of the center on the extended Dynkin diagram
added 85 characters in body
Mar
10
answered The action of the center on the extended Dynkin diagram
Mar
10
comment Deforming a basis of a polynomial ring
I think $a=0$ is triangular one way, $b=0$ triangular the other way. The one-box rule is here: mathoverflow.net/questions/88569/…
Mar
10
awarded  Nice Question
Mar
10
revised Deforming a basis of a polynomial ring
added 5 characters in body
Mar
10
asked Deforming a basis of a polynomial ring
Mar
9
awarded  Nice Answer