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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Homological Mirror Symmetry and Tropical Geometry (Paperback, 2014)
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Homological Mirror Symmetry and Tropical Geometry (Paperback, 2014)
Series: Lecture Notes of the Unione Matematica Italiana, 15
Expected to ship within 10 - 15 working days
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The relationship between Tropical Geometry and Mirror Symmetry goes
back to the work of Kontsevich and Y. Soibelman (2000), who applied
methods of non-archimedean geometry (in particular, tropical
curves) to Homological Mirror Symmetry. In combination with the
subsequent work of Mikhalkin on the "tropical" approach to
Gromov-Witten theory and the work of Gross and Siebert, Tropical
Geometry has now become a powerful tool. Homological Mirror
Symmetry is the area of mathematics concentrated around several
categorical equivalences connecting symplectic and holomorphic (or
algebraic) geometry. The central ideas first appeared in the work
of Maxim Kontsevich (1993). Roughly speaking, the subject can be
approached in two ways: either one uses Lagrangian torus fibrations
of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow
picture, further developed by Kontsevich and Soibelman) or one uses
Lefschetz fibrations of symplectic manifolds (suggested by
Kontsevich and further developed by Seidel). Tropical Geometry
studies piecewise-linear objects which appear as "degenerations" of
the corresponding algebro-geometric objects.
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