Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability

  title={Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability},
  author={Sean Timothy Paul and Kyriakos Sergiou},
  journal={Geometric Analysis},
Inspired by Gang Tian’s work in [4, 10, 11], and [12] we exhibit a wide range of energy functionals in Khler geometry as Fourier–Mukai transforms. Consequently these energies are completely determined by dual type varieties and therefore have logarithmic singularities when restricted to the space of algebraic potentials. This paper is dedicated to Gang Tian on the occasion of his 60th birthday. 
1 Citations

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