Finite generation of the algebra of type A conformal blocks via birational geometry

2017/09/02 by Moon, Han-Bom, Yoo, Sang-Bum
#14D20 #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1709.00519

Abstract

We study 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 which was previously obtained by Belkale. For each big divisor, the associated birational model is described in terms of moduli space of parabolic bundles.

Related

• Compactifications of moduli of G-bundles and conformal blocks
• Birational Geometry of the Space of Complete Quadrics
• The Algebra of Conformal Blocks
• Birational geometry of hypersurfaces in products of projective spaces
• Conformal Blocks in type C at level one