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
no code implementations • 21 Dec 2020 • Chin-Yu Hsiao, George Marinescu, Huan Wang
We establish Szeg\H{o} kernel asymptotic expansions on non-compact strictly pseudoconvex complete CR manifolds with transversal CR $\mathbb{R}$-action under certain natural geometric conditions.
Complex Variables Differential Geometry
no code implementations • 13 Jun 2019 • Chin-Yu Hsiao, Xiaonan Ma, George Marinescu
Let $X$ be a compact connected orientable CR manifold of dimension greater than five with the action of a connected compact Lie group $G$.
Complex Variables Differential Geometry
