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Results tagged with abelian-varieties
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user 439
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.
16
votes
Accepted
"Albanese" schemes: When does an "initial abelian scheme" exist under a given scheme?
The construction of an Albanese scheme and an Albanese map for proper and geometrically irreducible schemes over a perfect field goes back to the work of Chevalley, to this talk of Serre, and to Groth …
- 6,239
2
votes
morphisms from abelian varieties to rational curves.
Something is wrong with this statement: your map to $\mathbb{P}^{1}$ is given by a pencil in a linear system $|L|$ on $A$. Since the vector space dimension of the linear system is at least two it foll …
- 6,239
15
votes
Accepted
When is an Albanese variety principally polarized?
In general it could happen that the Albanese variety does not admit a principal polarization at all. For instance the Albanese variety of an abelian variety is the Abelian variety itself. So choose $X …
- 6,239