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Results tagged with complex-geometry
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user 151501
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.
7
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0
answers
244
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Triviality, ampleness, nefness, and bigness of the tangent bundle
Let $X$ be a smooth projective connected variety over $\mathbb{C}$ and let $T_X$ be its tangent bundle.
If $T_X$ is ample, then $X$ is isomorphic to a projective space by Mori's theorem.
If $T_X$ is t …
- 513
6
votes
0
answers
130
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Sections of infinite order of elliptic surfaces
Let $X\to \mathbb{P}^1$ be a non-isotrivial elliptic surface over $\mathbb{C}$ with a section and with $X$ a smooth projective connected surface over $\mathbb{C}$. Let $\sigma:\mathbb{P}^1\to X$ be a …
- 513
3
votes
1
answer
197
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Surfaces of general type with $q=1$
Let $X$ be a smooth projective connected surface of general type over $\mathbb{C}$ with $q(X) = 1$, where $q(X) = \mathrm{h}^1(X,\mathcal{O}_X)$.
Let $E$ be the Albanese variety of $X$, and let $X\to …
- 66.3k
2
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0
answers
183
views
Structure of non-big divisors in an abelian variety
Let $A$ be an abelian variety over $\mathbb{C}$. If $A$ has an effective non-big divisor, then $A$ is not simple. (In a simple abelian variety, every non-zero effective divisor is ample.)
What can …
- 513
5
votes
1
answer
138
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How to properly verify that $E\times E'$ has no non-trivial effective divisors with Kodaira ...
Let $E$ and $E'$ be elliptic curves over $\mathbb{C}$. I am pretty confident that the only effective divisor $D\subset E\times E'$ with Kodaira dimension zero is the trivial divisor.
How to prove th …
- 149k