Abstract This paper is devoted to the study of asymptotics Monge–Ampère volumes direct images associated with high tensor powers an ample line bundle. We leading term this and provide a classification bundles saturating topological bound Demailly. In special case symmetric vector bundles, provides characterization those admitting projectively flat Hermitian structures.

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the one constructed previ...

We will show that a statistical manifold $$(M, g, \nabla )$$ has constant curvature if and only it is projectively flat conjugate symmetric manifold, is, the affine connection $$\nabla $$ curvatures satisfies $$R=R^*$$ , where $$R^*$$ of dual ^*$$ . Moreover, we properly convex structures on compact induces $$-1$$ vice versa.

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth functions on the cotangent bundle, fiberwise-polynomial of bounded degree, a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the on...

We consider a family of fermionic star products generalising the Moyal product. The parameter space contains polarisations used to define quantum Hilbert spaces in geometric quantisation. For each polarisation, we find product functions on states and show that any function state remains state. establish associativity such products, which yields representations algebras spaces. is compatible wit...