0
votes
2answers
64 views
open immersion between affine spaces
Let $j:\mathbb{A}^{n}\rightarrow\mathbb{A}^{n}$ an open immersion over a field $k$. Is it an isomorphism?
0
votes
1answer
67 views
Surjectivity of the Gysin morphism
Let $f:X \to Y$ be a closed immersion between smooth projective complex varieties. Suppose that the codimension of (the image of) $Y$ in $X$ is equal to $r \ge 1$. This induces the …
1
vote
0answers
65 views
Existence of particular embeddings in euclidean spaces for non compact manifolds
Let $M$ be a $n$-dimensional smooth connected not compact manifold s.t. groups (singular cohomology)
$H^{k}(M,\mathbb{Z})$ are finitely generated for $k\geq 0$. Can we find …
0
votes
0answers
4 views
Smoothness and curvature of geodesics in a length space
Let $X$ be a nice compact subset of $R^d$. Given a function $p: X \to R^+$, define the length of a path $\gamma \subset X$ as $\ell(\gamma) = \int_\gamma p(x) dx$, and the distance …
4
votes
3answers
166 views
The “right” $C^*$ algebraic proof of Bott Periodicity
In learning about the K-theory of $C^*$-algebras, I have encountered the following 3 proofs of Bott periodicity:
$\bullet$ An argument based on Moyal quantization found in "Elemen …
10
votes
2answers
412 views
Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?
QUESTION
I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to …
1
vote
0answers
103 views
Why does Grothendieck’s period conjecture imply Hodge’s conjecture ?
Hello to all of you :
I would like to know if it is true that the Grothendieck period conjecture implies the Hodge conjecture in the case of non-singular complex algebraic varietie …
7
votes
2answers
183 views
Varieties which become isomorphic to algebraic groups over an algebraic closure
My question is as follows:
Let $k$ be a field of characteristic zero and let $\overline{k}$ be an algebraic closure. Let $V$ be an algebraic variety over $k$ and let $\overline …
3
votes
1answer
122 views
Strong Whitney embedding theorem for non-compact manifolds
$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact man …
1
vote
0answers
84 views
Laplacian for diffeomorphisms
Can one define Laplacian for a diffeomorphism from a Riemannian manifold to another Riemannian manifold? If yes, what kind of object is that?
0
votes
2answers
177 views
blow-ups and singularities
Let $X$ be a smooth and projective variety over a field of characteristic zero. Let $Y$ be a normal variety, with finite quotient singularities (an orbifold!) and let $\pi: Y \to X …
0
votes
1answer
103 views
First Chern class of canonical bundle ?
This is a somewhat simple question: consider a complex manifold $M$ and its canonical bundle $\omega_X$. It is clear that in $H^2(X,\mathbb{R})$,
$$c_1(\omega_X) = - c_1(T_X)$$
(O …
0
votes
0answers
102 views
Reference request for differential geometry [closed]
I have a somewhat bizzare question . I'm studying differential geometry for it's applications in physics . I'm interested in applying my knowledge to concrete objects . For example …
3
votes
1answer
84 views
Families of Hurwitz Curves
Hurwitz's theorem on automorphisms tells us that the group of automorphisms of a nonsingular complex algebraic curve of genus at least 2 is bounded above by $84(g-1)$ where $g$ is …
0
votes
1answer
109 views
When is an ample line bundle on an abelian variety base point free?
So, any line bundle $L$ on an abelian variety $X$ determines a type $(d_1,\ldots,d_g)$ where $d_i|d_{i+1}$. It's well known that if $d_1\geq 3$ then $L$ defines an embedding, that …
