Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with complex-geometry
Search options answers only
not deleted
user 10076
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
22
votes
flatness in complex analytic geometry
Mohammad,
flatness is not simple, so you are not going to get a simple overall definition. On the other hand, in the example you mention in your comment, there is a simple criterion:
Let $f:X\to …
- 42.9k
14
votes
Accepted
Hodge theory on complex spaces
Let me add to Donu's mentioning Du Bois's Hodge decomposition. First of all, many feel that part of the credit is due to Deligne as Du Bois built heavily on his ideas. Then again that is probably true …
- 42.9k
14
votes
Accepted
Generalisations of Riemann-Roch for surfaces
If $X$ is proper with rational singularities (and quotient and A-D-E (=Du Val) singularities are rational), then you can do most cohomology computations on a resolution.
Let $\pi:Y\to X$ be a resoluti …
- 42.9k
13
votes
Trying to Understand Lefschetz Pencils
Note: I am using the word "smooth" in the sense of algebraic geometry. For a differential geometer it would be "submersion". If by "smooth" you mean $C^\infty$, then every map is smooth here (so there …
- 42.9k
11
votes
Intuition behind the Kodaira Vanishing Theorem?
Here are some thoughts. For simplicity I will call a line bundle positive if it admits a metric as you described.
According to Serre's vanishing theorem for any (fixed) coherent sheaf $F$, the sheaf …
- 42.9k
10
votes
Accepted
Additivity of Kodaira dimension for a nice fibration
There is another inequality which says the following:
Easy addition
(Using the same notation):
$$
\kappa(X)\leqslant \kappa(X_y) + \dim Y
$$
Consequently, if $Y$ is of general type, i.e., $ …
- 42.9k
9
votes
Accepted
How many points determine a line?
As Artie points out, you can't do this with actual lines, but the next best thing is to ask the question with rational curves of minimal degree. If you have lines those will automatically be of minima …
- 42.9k
9
votes
Accepted
how to prove the following fact in sheaf cohomology ?
$\dim\mathrm{Supp}\\, \mathfrak F=0$ implies that $\mathfrak F\otimes \mathscr O_X(L)\simeq \mathfrak F$ and hence its cohomology is independent of $L$.
- 42.9k
9
votes
Accepted
Surgery in complex geometry
There is an operation in algebraic geometry, called a flip, which is a (kind of a special) surgery, so one could say that you hear about it, but under a different name. You can see the definition of a …
- 42.9k
9
votes
Accepted
Morphism between projective varieties
Here is an attempt to prove Angelo's comment (it seems too simple to use a reference for it):
$X,Y$ defined over $S$. If they are both proper over $S$, then so is $f$ by Hartshorne, II.4.8(e). In par …
- 42.9k
9
votes
Accepted
Is the set of surfaces over Spec Z with ample canonical sheaf empty
I don't think the answer to the first question is known.
Will has already pointed out the trivial answer to the second question. However this is not the right question. I mean this is kind of trivia …
- 42.9k
8
votes
Accepted
Uniformity of ampleness
Remark: If $p=q$, then one can just work with $E_p$ instead of $2E_p$ and then at the end take $2k_0$ instead of $k_0$, so we may assume that $p\neq q$ and in particular that the exceptional diviso …
- 42.9k
8
votes
in the analytic category, finite morphisms are open maps?
Open Mapping Theorem [Grauert-Remmert: Coherent analytic sheaves, p.107]
Let $X,Y$ be pure $d$-dimensional complex spaces and assume that $Y$ is locally irreducible. Then any holomorphic map $f:X\to Y …
- 42.9k
8
votes
Accepted
Basepoints in the canonical system of algebraic surfaces
In the general case when $n=\dim X$ is arbitrary
Kollár proves an analogue for minimal varieties of general type, although the bound is much worse than in the surface case.
In the situation at hand it …
- 42.9k
7
votes
Accepted
There are only finitely many varieties up to deformation
I believe the two things you are relating:
The finiteness of the
number of deformation types
number of components of the moduli space
of polarized varieties are essentially equivalent problems.
…
- 42.9k