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Results tagged with abelian-varieties
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user 70593
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.
6
votes
1
answer
247
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Are there curves of genus 2 with real multiplication by a non-maximal order?
Let us work over $\mathbb{C}$ for the moment.
Assume we are given a real quadratic field $K$ with ring of integers $\mathcal{O}_K$.
$\mathbf{Question:}$ Is there a smooth projective curve $C$ of gen …
- 1,025
0
votes
1
answer
149
views
Behaviour of (principal) polarizations of (singular) surfaces under birational maps
Assume we have two p.p. simple abelian surfaces $(A_i,D_i)$, i=1,2, over $\mathbb{C}$ with the following commutative diagram:
$\require{AMScd}
\begin{CD}
A_1 @>{birational}>> A_2\\
@V{2:1}VV @VV{2:1} …
- 1,025