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Asymptotic expansion of induced Grassmannian Chern forms and distribution of random degeneracy sets
Turgay Bayraktar, Dan Coman, Bingxiao Liu +1
The authors obtain a complete asymptotic expansion for Chern forms induced by Grassmannian embeddings of high‑tensor‑power holomorphic sections, and use it to prove that normalized…
Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for -concave domains
Bingxiao Liu, George Marinescu, Huan Wang
We consider a compact -dimensional complex manifold endowed with a holomorphic line bundle that is semi-positive everywhere and positive at least at one point. Additionally, we…
Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections
Turgay Bayraktar, Dan Coman, Bingxiao Liu +1
Let be a compact Kähler manifold, be a positive line bundle, and be a Hermitian holomorphic vector bundle of rank on . We prove that the pullba…
Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros
Bingxiao Liu, Dominik Zielinski
We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Rieman…
Toeplitz operators and zeros of square-integrable random holomorphic sections
Alexander Drewitz, Bingxiao Liu, George Marinescu
We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive li…