Symmetric products of surfaces distinguish two macroscopic dimension notions and address Gromov-Lawson and Gromov conjectures in the Kaehler projective setting while connecting to minimal models and positivity in algebraic geometry.
Symmetric products of surfaces; a unifying theme for topology and physics
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abstract
This is a review paper about symmetric products of spaces $SP^n(X):= X^n/S_n$. We focus our attention on the symmetric products of 2-manifolds and make a journey through selected topics of algebraic topology, algebraic geometry, mathematical physics, theoretical mechanics etc. where these objects play an important role, demonstrating along the way the fundamental unity of diverse fields of physics and mathematics.
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Curvature, macroscopic dimensions, and symmetric products of surfaces
Symmetric products of surfaces distinguish two macroscopic dimension notions and address Gromov-Lawson and Gromov conjectures in the Kaehler projective setting while connecting to minimal models and positivity in algebraic geometry.