Skip to main content
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
Search options not deleted user 392184

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.

4 votes
1 answer
391 views

Complex manifolds whose tangent and cotangent bundles are isomorphic as complex vector bundles

Question. What are examples of compact complex manifolds whose tangent and cotangent bundles are isomorphic as complex vector bundles? A family of examples are, of course, holomorphically symplectic m …
Jost Schultze's user avatar
12 votes
2 answers
723 views

Non-Kähler pseudo-Kähler manifolds

A pseudo-Kähler manifold is a complex manifold $(X, I)$ endowed with a non-degenerate closed $(1, 1)$-form $\omega$. In that case, the symmetric tensor $g(\cdot, \cdot) = \omega(\cdot, I \cdot)$ is a …
Jost Schultze's user avatar
6 votes
1 answer
207 views

Existence of a real structure on the tangent bundle of a complex manifold

Let $X$ be a compact complex manifold. What are obstructions to the existence of a real subbundle $V$ of $TX$ such that $TX = V \otimes \mathbb{C}$? For example, does $\mathbb{CP}^n$ have such a struc …
Jost Schultze's user avatar
4 votes
0 answers
120 views

Does unobstructedness depend on the representative of a Kodaira-Spencer class?

Let $X$ be a compact complex manifold. One says that a Kodaira-Spencer class $c \in H^1(X, TX)$ is unobstructed if there exist $\phi_n \in \Omega_X^{0,1}(T^{1,0}X)$ for $n \ge 1$ such that $c = [\phi_ …
Jost Schultze's user avatar
7 votes
1 answer
747 views

What is the definition of a Calabi-Yau metric on a non-compact manifold?

There is a lot of important recent work on the construction of Calabi-Yau metrics on non-compact complex manifolds, such as $\mathbb{C}^n$. For example: [1] Li, Y. A new complete Calabi-Yau metric on …
Jost Schultze's user avatar
3 votes
1 answer
355 views

Extension of closed $(1, 1)$-forms

Let $X$ be a compact Kähler manifold and $S \subset X$ a closed complex submanifold. Given a closed $(1, 1)$-form $\alpha$ on $S$, is there always a closed $(1, 1)$-form $\beta$ on a neighborhood of $ …
Jost Schultze's user avatar
9 votes
0 answers
379 views

Kähler metric on the Hilbert scheme of points on a surface

Question. Let $S$ be a non-singular complex projective surface and let $S^{[n]}$ be its Hilbert scheme of $n$ points. Is there a natural way to associate to a Kähler metric $\omega$ on $S$ a Kähler m …
Jost Schultze's user avatar