no code implementations • 28 Dec 2020 • Dan Coman, George Marinescu
We prove the convergence of the normalized Fubini-Study measures and the logarithms of the Bergman kernels of various Bergman spaces of holomorphic and weakly holomorphic sections associated to a singular Hermitian holomorphic line bundle on an algebraic curve.
Complex Variables Primary 32L10, Secondary 14H60, 30F10, 32U40
no code implementations • 22 Dec 2020 • Dan Coman, Wen Lu, Xiaonan Ma, George Marinescu
Given a sequence of positive Hermitian holomorphic line bundles $(L_p, h_p)$ on a K\"ahler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural convergence assumption on the sequence of curvatures $c_1(L_p, h_p)$.
Complex Variables Differential Geometry Probability Symplectic Geometry
