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Results tagged with complex-geometry
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user 57030
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
359
views
Kähler metric on compact complex manifolds with simple normal crossing divisor
Let $X$ be a reduced compact complex analytic space of $\dim_{\mathbb{C}}X\ge2$; by [KJ] definition 3.29, remark 3.44 and theorem 3.45, it admits a strong resolution $R(X)$ which is smooth, $E=\pi_X^{ …
- 828
1
vote
Exponential Sequence of Sheaves
Let $f\in\ker(\exp)$; by definition:
\begin{equation}
\forall x\in X,\,\exp_x(f_x)=1\in\mathcal{O}_{X,x}^{\times},
\end{equation}
in other words:
\begin{equation}
\exp_x(f_x)=\exp_x(Re(f_x))[\cos(Im(f …
- 828
1
vote
Accepted
Kähler metric on compact complex manifolds with simple normal crossing divisor
Without loss of generality, let $X$ be irreducible, then it is pure-dimensional ([GH,RR] proposition 9.1.3).
Let $\left(\widehat{X},\nu\right)$ be the normalization of $X$ ([FG] chapter 2, section 16 …
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0
votes
1
answer
174
views
BMY inequality for surfaces of general type in characteristic 0
Let $X$ be a smooth, complex, projective, minimal surface of general type, i.e. the canonical (line) bundle $K_X$ is big and nef.
It is known that $3c_2\geq c_1^2$ (the Bogomolov-Miyaoka-Yau inequalit …
- 828
6
votes
0
answers
195
views
Does there exist a notion of Chern classes in intersection cohomology?
First of all: I apologize for my mistakes, I'm a freshman in intersection cohomology.
Let $X$ be a (compact) complex analytic space, let $L$ be a line bundle over $X$.
Can one define a notion of f …
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4
votes
1
answer
305
views
Nef line bundles over complex analytic spaces
Let $L$ be a line bundle over a compact complex manifold $X$ with a Hermitian metric $\omega$: $L$ is said numerically effective (nef, for short) if for any $\epsilon>0$ there exists a smooth Hermitia …
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