The lattice points of a stacky polytope

Abstract

We study the relation between the lattice points of a stacky polytope and a prequantisation of the stack associated to the stacky polytope. We introduce a prequantisation of a Deligne--Mumford stack and discuss the uniqueness and the existence of a prequantisation. After that we describe explicitly the condition for the existence of a prequantisation in terms of stacky polytope under some conditions and discuss the relation between the holomorphic line bundle associated to a prequantisation and the lattice points of the stacky polytope.

20 pages

References in corpus (3)

• Topological and Smooth Stacks
• Riemann-Roch for Deligne-Mumford stacks
• On symplectic vortex equations over a compact orbifold Riemann surface