Monthly Archives: July 2012

Why are elliptic curves projective?

Before we go on to discuss what makes a complex torus algebraic, let us perhaps return to the case of elliptic curves. The claim is that all elliptic curves are algebraic; other than the one case explicitly provided in the … Continue reading

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Abelian varieties

We would like to generalize one of the nice properties of Elliptic curves, namely that maps between them are determined by linear Algebra: Specifically, sublattices of the lattice . To do so we must first introduce the notion of an … Continue reading

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On to higher genus curves

Let us summarize what we have discussed about Elliptic curves. First of all, we can parameterize Elliptic curves by either studying the moduli of lattices in the complex plane, or by looking at the Hodge decomposition of their first cohomology … Continue reading

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