bio  website  math.berkeley.edu/~achinger 

location  Berkeley  
age  28  
visits  member for  4 years, 11 months 
seen  2 hours ago  
stats  profile views  3,057 
PhD student, UC Berkeley
16h

awarded  Popular Question 
Jan 13 
comment 
Intersections of $B$ and $B^$ orbits in the flag variety $G/B$
It is also stated there that their closures are CohenMacaulay, so in particular they are equidimensional. 
Jan 13 
comment 
Intersections of $B$ and $B^$ orbits in the flag variety $G/B$
I think they are called (open) Richardson varieties. Their dimensions are described here: arxiv.org/pdf/1008.3939v2.pdf (page 2). 
Jan 12 
awarded  Guru 
Jan 8 
comment 
Is there a “simplification” functor in algebraic topology?
Universal in the homotopy category, I presume? 
Jan 8 
awarded  Taxonomist 
Dec 28 
comment 
Coherent sheaves on Proj
Note that q.c. sheaves on $Proj(S)$ are the same as $\mathbb{G}_m$linearized sheaves on $Spec(S)\setminus \{m\}$ where $m = \bigoplus_{n>0} S_n$ is the irrelevant ideal. So you are asking for a criterion for an $S$module $M$ being zero away from $m$. But this is equivalent to asking when $M_x = 0$ for each $x\in m$. So the criterion (for a f.g. module) is: iff $m^k M = 0$ for some $k>0$. This in turn is clearly equivalent to $M$ having only finitely many nonzero degrees. 
Dec 24 
comment 
Blowups of $\mathbb{P}^{n3}$ and $(\mathbb{P}^1)^{n3}$
It is indeed toric  it's the identity on the torus, and the analysis of fans is used to show that it extends to the open orbits of the boundary divisors. 
Dec 22 
comment 
Applications of $p$adic Hodge theory
The notes by Brinon and Conrad are great, but I personally didn't get much motivation out of them. "An abelian variety has good reduction if and only if the associated Galois rep is crystalline" didn't seem to me like a good enough "application", as the definition of "crystalline" is complicated. I'd love to see here, say, new theorems about varieties over $\mathbb{C}$ proved using $p$adic comparison theorems. 
Dec 22 
comment 
Futaki invariant on $X=Bl_p(\mathbb CP^2)$ for different line bundles
What is the Futaki invariant? 
Dec 22 
answered  Blowups of $\mathbb{P}^{n3}$ and $(\mathbb{P}^1)^{n3}$ 
Dec 21 
comment 
Blowups of $\mathbb{P}^{n3}$ and $(\mathbb{P}^1)^{n3}$
I assume you are asking whether $X$ and $Y$ are isomorphic away from a codim $\geq 2$ subset? 
Dec 9 
comment 
Morphism on schemes induced by continuous morphism of sites
Do you mean ringed topoi? 
Dec 5 
comment 
Rationality of moduli spaces of rational curves
@AbdelmalekAbdesselam good point! :D 
Dec 4 
comment 
Rationality of moduli spaces of rational curves
Maybe I'm wrong, but doesn't the following work? For $a_0, \ldots, a_{n1}\in k$, consider the subscheme of $\mathbb{A}^1_k$ given by $x^n + a_{n1}x^{n1} + \ldots + a_0 = 0$. For generic $a_i$, this is a collection of $n$ distinct points, so we get a rational map from $\mathbb{A}^n$ to $\tilde M_{0, n}$ which is actually birational (as it's dominant and injective). 
Dec 3 
comment 
Map of adjunctions
For me (an algebraic geometer), the natural setting would be a cartesian diagram of topoi, and in that case we would call the natural transformation the "base change" map. There are important cases where this map is an isomorphism, e.g. when the map $H$ is "proper" (this is the $q=0$ part of the proper base change theorem in SGA4). So I would try to characterize properness in categorytheoretic terms. 
Dec 1 
awarded  Good Answer 
Nov 26 
comment 
How to see that this pairing of line bundles is multiplicative?
But $F$ might not have a finite resolution by vector bundles unless $X$ is smooth projective... 
Nov 25 
comment 
How to see that this pairing of line bundles is multiplicative?
What is the definition of $\det(F)$? $F$ might not be a perfect complex... 
Nov 25 
awarded  Enlightened 