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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.
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does $Aut^0$ act trivially on the Neron-Severi group?
Let $X$ be a projective integral scheme over an algebraically closed field $k$. Does $\mathrm{Aut}^0_{X/k}(k)$ act trivially on $NS(X)$?
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Does cohomology with compact support contain "ample" elements
Let $X$ be a quasi-projective integral variety over $\mathbb{C}$. If $X$ is projective, then $\mathrm{H}^2(X,\mathbb{Z})$ contains "ample" classes. These "ample" classes are defined as being the image …