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Results tagged with ag.algebraic-geometry
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user 22823
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
8
votes
1
answer
2k
views
Line bundles and vector bundles on $\mathbb P^1 \times \mathbb P^1$
Is there a classification of vector bundles on $\mathbb P^1 \times \mathbb P^1$? I know that the analogue of Grothendieck's splitting theorem is not true for $\mathbb P^1 \times \mathbb P^1$.
Is it …
- 135
3
votes
1
answer
2k
views
When does a finite morphism induce isomorphism on cohomology?
Let $Y \to X$ be a finite morphism of schemes of dimension $n$. The induced map on the top cohomology $H^n(X, \mathcal O_X) \to H^n(Y, \mathcal O_Y)$ is always surjective. When is it injective? Can …
- 135
1
vote
1
answer
836
views
Homological equivalence for algebraic cycles
How does one prove that for a smooth projective variety $X$ over an algebraically closed field $k$, an algebraic cycle that is homologically equivalent to zero is also numerically equivalent to zero? …
- 135
1
vote
1
answer
1k
views
Birational maps and Picard groups
Suppose $X$ and $Y$ are curves, and suppose $f: Y \to X$ is a birational map. If $f$ is bijective on geometric points, what can be said about the induced map on the Picard groups $Pic(X) \to Pic(Y)$ …
- 135