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Results tagged with ag.algebraic-geometry
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user 20562
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
3
votes
divisor is big iff its birational pullback is big
In this book Kollar and Mori define big divisors only for proper (irreducible) varieties, so when they say that for a birational morphism $f:X\to Y$, the pullback $f^*D$ of a divisor $D$ on $Y$ is bi …
- 304
2
votes
Accepted
Map to a given vector bundle from a split vector bundle
Yes. Slightly more precisely, we have the following result.
Proposition: Let $X$ be a normal, integral, finite-type scheme over a field.
Let $F$ be a locally free $\mathcal O_X$-module of finite …
- 304
13
votes
Higher dimensional version of the Hurwitz formula?
Here is a lighthearted attempt at generalizing the discussion of Hurwitz' formula in Hartshorne to higher dimensions.
Let $f:Y\to X$ be morphism of schemes over a field $k$. Assume that $X$ and $Y$ a …
- 304