A compact prequantized symplectic manifold with a Lagrangian torus fibration has Riemann-Roch number equal to its number of Bohr-Sommerfeld fibers, proved via a new theorem: volume equals number of integer points on compact integral-integral affine manifolds.
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Integral-integral affine geometry, geometric quantization, and Riemann-Roch
A compact prequantized symplectic manifold with a Lagrangian torus fibration has Riemann-Roch number equal to its number of Bohr-Sommerfeld fibers, proved via a new theorem: volume equals number of integer points on compact integral-integral affine manifolds.