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Results tagged with ag.algebraic-geometry
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user 75200
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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rationality of residues of differentials
Let $C$ be a smooth curve over a field $k$, $\overline{C}$ the smooth compactification and $S=\overline{C} \setminus C$. We think of $S$ as a reduced divisor defined over $k$. Take the sheaf of logari …
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meaning of $k$-rational for closed subschemes
Let $X$ be a variety over a field $k$. I know the definition of $k$-rational point: a closed point $x$ is $k$-rational if its residue field $k(x)$ is equal to $k$ (in general, $k(x)$ is only a finite …
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Kummer theory and ramified covers
Let $X \to Y$ be a cyclic cover of algebraic varieties, with $Y$ smooth and $X$ normal, say over the complex numbers. Let $G$ denote the Galois group and let $\chi$ be a character. By Kummer theory (a …
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