Abstract:The existence of smooth solutions to a broad class of complex Hessian type equations is related to nonlinear Nakai type criteria on intersection numbers on Kahler manifolds. Such a Nakai criteria can be interpreted as a slope stability condition analogous to the slope stability for Hermitian vector bundles over Kahler manifolds. In the present work, we initiate a program to find canon...
Abstract:In this talk, we will discuss recent advancements in the specialization of linear differential equations. Given a linear differential equation with parameters, our focus is on how the algebraic properties of its solutions change as these parameters vary over an affine variety. For example, we inquire about the values of parameters for which linear differential equations can have a basi...