Finite Generation of the Algebra of Type A Conformal Blocks via Birational Geometry

@article{Moon2018FiniteGO,
  title={Finite Generation of the Algebra of Type A Conformal Blocks via Birational Geometry},
  author={Han-Bom Moon and Sang-Bum Yoo},
  journal={International Mathematics Research Notices},
  year={2018}
}
We study the birational geometry of the moduli space of parabolic bundles over a projective line, in the framework of Mori’s program. We show that the moduli space is a Mori dream space. As a consequence, we obtain the finite generation of the algebra of type A conformal blocks. Furthermore, we compute the H-representation of the effective cone that was previously obtained by Belkale. For each big divisor, the associated birational model is described in terms of moduli space of parabolic… 
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