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bio website math.berkeley.edu/~achinger
location Berkeley
age 28
visits member for 4 years, 11 months
seen 2 hours ago
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 Cohen-Macaulay, so in particular they are equi-dimensional.
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 Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$
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 Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$
Dec
21
comment Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$
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 $a_0, \ldots, a_{n-1}\in k$, consider the subscheme of $\mathbb{A}^1_k$ given by $x^n + a_{n-1}x^{n-1} + \ldots + a_0 = 0$. 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 category-theoretic 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