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Results tagged with abelian-varieties
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user 3377
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.
0
votes
Moduli space of complex and anti-complex tori?
For $d$ odd these two components are disconnected, because $I$ and $-I$ induce opposite orientation. For $d$ even, you have an involution, which takes a lattice to a complex conjugate lattice. This in …
- 12.9k
6
votes
Accepted
Dual of a Complex 2-Torus
For non-algebraic tori, $T$ and $T^*$ are (usually) not isomorphic; for algebraic ones, they are isogeneous, and for the principally polarized abelian varieties, $T$ and $T^*$ are isomorphic.
This i …
- 9,237
2
votes
Quotient of an abelian surface by an antisymplectic involution
Averaging a Kaehler class over the involution, and taking
the corresponding Ricci-flat metric, we may assume that
the involution preserves a flat metric on a torus.
At each fixed point, the eigenvalu …
- 9,237