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 not deleted
user 3709
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.
1
vote
0
answers
123
views
Is every curve on a projective three-fold a homology-theoretic complete intersection of sorts?
Let $C$ be a curve on a smooth projective three-fold $M$ equipped with the restriction of the Fubini-Study metric $\omega$. I'd like to know if there exists a surface $S$ such that for every closed $( …
- 3,383
2
votes
0
answers
84
views
Green’s function vector bundle laplacian
On a compact Riemann surface with a metric, there exists a Green’s function $C ln(d(x,y)^2)\leq G(x,y)\leq 0$ satisfying $u=\int u+ \int G(x,y) u(y) dy$.
Suppose $(E,h)$ is a Hermitian holomorphic bu …
- 3,383
2
votes
0
answers
114
views
Equivariant resolution of singularities with equivariant centres
From what I understand, given a complex projective variety X inside a compact complex manifold Y, according to Hironaka, there is a sequence of $r$ blowups $Y_i$ of Y along complex submanifolds (centr …
- 3,383
4
votes
1
answer
215
views
Examples of surfaces with negative Kahler curvature operator
Compact ball quotients are examples of compact Kahler surfaces with negative curvature operator.
Are there any other examples ? What about nonpositive (other than the product of two Riemann surfaces …
- 7,902
20
votes
5
answers
7k
views
Griffiths and Harris reference
Trying to read the section on Poincare duality from Griffiths and Harris is a nightmare. I want to know if there is a place where Poincare duality and intersection theory are done cleanly and rigorous …
- 101
10
votes
0
answers
342
views
Local meaning of the Pfaffian of the curvature
The Ricci and scalar curvatures have very nice pointwise interpretations (using the local expression for the volume form for example). So, (at least Ricci) having special metrics (like Einstein) can p …
- 3,383
4
votes
0
answers
189
views
Chern-Weil theory for coherent subsheaves
If $(E,h)$ is a holomorphic vector bundle over a compact complex manifold $M$ (which is a projective variety), and $S$ is a coherent subsheaf of $M$, then $S$ is secretly a holomorphic vector bundle o …
- 3,383
2
votes
0
answers
166
views
Why only the first two Chern classes in the BMY and KL inequalities?
The Bogomolov-Miyaoka-Yau inequality for compact complex manifolds with ample canonical bundle and the Kobayashi-Lubke inequality for holomorphic stable vector bundles involve the first two Chern clas …
- 3,383
2
votes
1
answer
217
views
Number of semistable subbundles of a semistable bundle
Is the following true ? If so, is there a quick proof of it ? (Perhaps using the uniqueness of the graded object associated to a Jordan-Holder filtration or maybe otherwise)
Suppose $E$ is an $\omega …
- 4,111
1
vote
0
answers
140
views
Equivariant Kodaira embedding
Suppose $X$ is a compact complex manifold acted upon by biholomorphisms by a complex Lie group. Suppose $L$ is an equivariant line bundle which is also ample (in the sense that it admits an equivarian …
- 3,383
5
votes
1
answer
1k
views
Quillen metric definition
I am confused as to why a regularised determinant is used in the definition of Quillen's metric on the determinant line bundle defined over the space of $\bar{\partial}$ operators on a (hermitian) vec …
- 6,259
12
votes
2
answers
541
views
Relationship between the Radon transform and Twistor spaces
I have often heard that the theory of Twistor spaces is ``a complex analogue" of the Radon transform. What is the precise connection ?
- 188k
1
vote
1
answer
383
views
Holomorphic h-principle for compact manifolds
The Oka principle for Stein manifolds says (roughly) that the only obstructions for "things" are topological obstructions (for instance every smooth complex vector bundle admits a holomorphic structur …
- 39.1k
11
votes
2
answers
3k
views
$\partial \bar{\partial}$ lemma for contractible domains
Question. Is every $(p, \, p)$ closed form ($p\geq1$) in a contractible open set of $\mathbb{C}^n$ $\partial \bar{\partial}$ exact?
We know that every $d$-exact $(p, \,p)$-form on a compact Kahl …
- 66.3k
1
vote
0
answers
97
views
Systematic way of finding balanced metrics
In several PDE involving metrics (like the Hermite-Einstein equation for vector bundles and the constant scalar curvature Kahler equation for manifolds) there is a notion along these lines - If a solu …
- 3,383