We use a relative Fourier-Mukai transform on elliptic K3 surfaces X to describe mirror symmetry. The action of this Fourier-Mukai transform on the cohomology ring of X reproduces relative T-duality and provides an infinitesimal isometry of the moduli space of algebraic structures on X which, in view of the triviality of the quantum cohomology of K3 surfaces, can be interpreted as mirror symmetry. From the mathematical viewpoint the novelty is that we exhibit another example of a Fourier-Mukai transform on K3 surfaces, whose properties are closely related to the geometry of the relative Jacobian of X.
Mirror symmetry on K3 surfaces via Fourier-Mukai transform / Bartocci, C.; Bruzzo, U.; Hernandez-Ruiperez, D.; Munoz Porras, J. M.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 195:1(1998), pp. 79-93. [10.1007/s002200050380]
Mirror symmetry on K3 surfaces via Fourier-Mukai transform
Bruzzo, U.;
1998
Abstract
We use a relative Fourier-Mukai transform on elliptic K3 surfaces X to describe mirror symmetry. The action of this Fourier-Mukai transform on the cohomology ring of X reproduces relative T-duality and provides an infinitesimal isometry of the moduli space of algebraic structures on X which, in view of the triviality of the quantum cohomology of K3 surfaces, can be interpreted as mirror symmetry. From the mathematical viewpoint the novelty is that we exhibit another example of a Fourier-Mukai transform on K3 surfaces, whose properties are closely related to the geometry of the relative Jacobian of X.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
