All Questions
Tagged with analytic-geometry dg.differential-geometry
7
questions
19
votes
1
answer
2k
views
When do real analytic functions form a coherent sheaf?
It is known that, in general, the sheaf of real analytic functions on a real analytic manifold is not coherent. However, there are some examples, where we have coherence: for example, if $X$ is a ...
- 1,234
5
votes
2
answers
529
views
When is a real-analytic variety a union of non-singular subvarieties?
I have asked this before on MSE, but received no answer yet.
Say I have a set in $\mathbb{R}^n$ defined to be the zero set of an analytic function $F:\mathbb{R}^n\to\mathbb{R}^k$, $k<n$. Everywhere,...
- 212
4
votes
1
answer
440
views
Origin of 'Analytic' Geometry?
My impression is that the name analytic geometry, which I understand roughly to be geometry in Euclidean space using coordinates, is not used that much anymore. We would probably classify the subject ...
- 13.4k
4
votes
0
answers
159
views
Sheaf of smooth functions and restriction to a divisor
My question is targeted towards a very particular detail in my research that I am trying to understand. I will therefore break it down into some more general questions.
Let $X$ be a smooth variety, $i:...
- 914
3
votes
2
answers
588
views
If $K$ and $L$ are compact convex sets with smooth boundary, does their union have piecewise-smooth boundary?
Clarification: by "piecewise", I mean a finite number of pieces.
I'm sure this must be true, but my search for a citation was in vain (although I did learn the new term "polyconvex").
Thanks!
- 6,531
3
votes
1
answer
384
views
about transverse complete intersection
There are several questions about transverse complete intersection arising from L. Guth's paper:
http://www.ams.org/journals/jams/0000-000-00/S0894-0347-2015-00827-X/home.html
We say a polynomial $P$...
- 103
2
votes
1
answer
343
views
Is the closure of an open holomorphically convex subset of a Stein space holomorphically convex?
Let X be a Stein manifold and U an open, connected, relatively compact, holomorphically convex subset of X. Is the closure of U in X holomorphically convex?
Also, if X is a Stein space with a finite ...
- 169