Tagged Questions
2
votes
1answer
37 views
On the definition of divisors in Riemann Surfaces
The sum notation for a Divisor $D$ in a Riemann Surface $X$ (as in Miranda's "Algebraic Curves and Riemann Surfaces") is
$$
D=\sum_{p\in X} D(p)\cdot p
$$
That is, $D$ assumes the value $D(p)$ at $p$. ...
4
votes
2answers
89 views
Definition of Unipotent in Positive Characteristic
Let $G$ be an affine algebraic group over an algebraically closed field $k$ whose characteristic is $p>0$. Can $\mathcal{U}(G)$, the set of unipotent elements of $G$, be characterized as all ...
2
votes
3answers
111 views
Definition of degree of finite morphism plus context
Let $f: X \rightarrow Y$ be a finite morphism of schemes, defined here,
http://en.wikipedia.org/wiki/Finite_morphism
I always assumed that the degree of $f$ was the degree of the induced field ...
1
vote
1answer
130 views
Definition of the Ideal Sheaf
Let $Y$ be a closed subscheme of a scheme $X$ and let $i:Y \rightarrow X$ be the inclusion morphism. Then the ideal sheaf of $Y$ is defined to be the kernel of the morphism of sheafs $i^{\#}: ...
2
votes
1answer
60 views
Separated and Finite Type Scheme over an Algebraically Closed Field
Let $(X,\mathcal{O}_X)$ be a separated scheme and of finite type over an algebraically closed field $k$. The fact that $X$ is separated means that the image of $X$ under the diagonal morphism $\Delta: ...
0
votes
0answers
42 views
What is $Pic(S)^G?$
Let $S$ be a projective surface and $\text{Pic}(S)$ its Picard group, $G$ is some group (in fact, it consists of automorpisms of $\mathbb P^2$). I came across a notation "$\text{Pic}(S)^G$". Could you ...
1
vote
1answer
81 views
Definition of tautological section.
Reading Barth, Peters: Compact complex surfaces, i stumbled across the following:
Let $Y$ be an algebraic surface over $k =\mathbb{C}$, and $\mathcal{L}$ an invertible sheaf on $Y$. Denote by $p: L ...
3
votes
1answer
255 views
“sheaf” au sens de Serre
I learned the definition of sheaves from Algebraic Geometry by Hartshorne, while reading Serre's GAGA, I was wondering if there was another definition of sheaves. [Here is the link of the English ...
4
votes
1answer
79 views
intrinsic and geometric definition of blow-up
Suppose I am given an algebraic variety $X$ and a (closed) point $x \in X$. I know of two descriptions of the blow-up of $X$ at $x$. One is intrinsic but not geometric: if $\mathcal{I}_x$ denotes the ...
3
votes
0answers
68 views
Closed / embedded surface
Given a closed surface in $\mathbb R^3$, is it necessarily an "embedded surface"? I think it is true, but that is just because I can't think of a closed surface for which we cannot construct a smooth ...
5
votes
1answer
294 views
Why does the definition of an open subscheme / open immersion of schemes allow for an “extra” isomorphism?
After taking an algebraic geometry course last year, I've been reviewing the material this year, and I remembered something that struck me as odd, but which I'd neglected to ask about at the time:
...
7
votes
3answers
510 views
What is the operation $\boxtimes$?
Reading papers about $p$-adic analysis and Galois representations, I have found objects like this $D \boxtimes \mathbb{Q}_p$. So my question is what is $\boxtimes$ and how do we read it ?
