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August 2006 Seidel's mirror map for abelian varieties
Marco Aldi, Eric Zaslow
Adv. Theor. Math. Phys. 10(4): 591-602 (August 2006).


We compute Seidel’s mirror map for abelian varieties by constructing the homogeneous coordinate rings from the Fukaya category of the symplectic mirrors. The computations are feasible, as only linear holomorphic disks contribute to the Fukaya composition in the case of the planar Lagrangians used. The map depends on a symplectomorphism ρ representing the large complex structure monodromy. For the example of the two-torus, different families of elliptic curves are obtained by using different ρ’s which are linear in the universal cover. In the case where ρ is merely affine linear in the universal cover, the commutative elliptic curve mirror is embedded in noncommutative projective space. The case of Kummer surfaces is also considered.


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Marco Aldi. Eric Zaslow. "Seidel's mirror map for abelian varieties." Adv. Theor. Math. Phys. 10 (4) 591 - 602, August 2006.


Published: August 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1101.81083
MathSciNet: MR2259690

Primary: 14J32
Secondary: 53D40

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 4 • August 2006
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