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Results tagged with abelian-varieties
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user 46104
Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
2
votes
Accepted
Pullback of line bundles and divisors from $Kum(C)$ to $Jac(C)$
1) is correct, 2) is not.
Indeed, if $i(C)=C$, then the map $C \rightarrow C'$ is a double cover, and $f^*{\mathcal O}_Y(C')={\mathcal O}_X(C)$ since in a neighbourhood of a general point of $C$ the …
- 1,054
5
votes
Accepted
Will any two linearly equivalent ample divisors on an abelian variety intersect?
Of course not.
If $L$ is very ample, $D_1$ and $D_2$ are two hyperplane sections for some embedding in a projective space. Therefore their intersection is at most codimension 2 in $X$, intersection o …
- 1,054