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Results tagged with abelian-varieties
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user 4096
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
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equation for abelian varieties with a given polarization
Let $A$ be an abelian variety of dimension g and a polarization $L$ of type $(d_1,.....,d_g)$ (let alone the case $d_i=d_j,$ $\forall i, j$). What is the degree of the generators of the homogeneous id …
- 3,779
4
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1
answer
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(3,3) abelian surface and k3 surfaces
SOrry for the very specific question, but curiosity bites....
So here's the story: an idecomposable principally polarized abelian surface is embedded in $P^8=|3\Theta |^* $ as a deg 18 surface A. Mo …
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0
answers
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symmetric theta structures and arithmetic subgroups
A symmetric theta structure is a theta structure that commutes with (a lift of) the natural involution $\imath: A \to A$ an an abelian variety. For simplicity I will assume that $A$ is a surface.
Now …
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0
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Action of $(\mathbb{Z}/2g\mathbb{Z})$ on quadratic forms on $\mathbb{Z}/2\mathbb{Z}$-vector ...
Let $\mathbb{Z}/2\mathbb{Z}$ the 2 elements field, with additive notation.
I need some clarifications on the relation between quadratic forms on a $\mathbb{Z}/2\mathbb{Z}$-vector space (say, of dimen …
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2
votes
1
answer
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Fiber of the Prym map in dim 2
This must be very classical, but I can't find a reference.
Is there an explicit description of the (generic?) fibers of the Prym map $\mathcal{R}_3 \to \mathcal{A}_2$?
By this I mean the map t …
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Accepted
On morphisms to projective space arising from a linear system
$E$ can't intersect $C$ in a finite number of points because otherwise the restriction of $\phi$ to $C$ would be a finite degree morphism, which you assume is not. $E$ is the pull-back of the hyperpla …
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quasi-trigonal curves
I have read in the literature about quasi-trigonal curves. Such a curve C is a hyperelliptic curve X with two points p,q identified (basically a pinch). They seem to be pretty important in the theory …
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