Finite TYCZ expansions and cscK metrics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Loi, Andrea¹  Mossa, Roberto²  Zuddas, Fabio³ 

[1] Univ Cagliari, Dipartimento Matemat, Cagliari, Italy

[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, Brazil

[3] Univ Cagliari, Dipartimento Matemat & Informat, Cagliari, Italy

关键词: TYCZ expansion;    Szego kernel;    Log-term;    Kempf distortion function;    Radial potential;    Constant scalar curvature metric;   

DOI  :  10.1016/j.jmaa.2019.123715

来源: Elsevier

【 摘 要 】

Let (M, g) be a Kahler manifold whose associated Kahler form omega is integral and let (L, h) -> (M, omega) be a quantization hermitian line bundle. In this paper we study those Kahle': manifolds (M, g) admitting a finite TYCZ expansion, namely those for which the associated Kempf distortion function T-mg is of the form: T-mg (p) = f(s) (p)m(s) + f(s-1) (p)m(s-1)+ . . . + fr(p)m(T), f(j) is an element of C-infinity(M), s, r is an element of Z. We show that if the TYCZ expansion is finite then T-mg is indeed a polynomial in m of degree n, n = dim(C) M, and the log-term of the Szego kernel of the disc bundle D C L* vanishes (where L* is the dual bundle of L). Moreover, we provide a complete classification of the Kdhler manifolds admitting finite TYCZ expansion either when M is a complex curve or when M is a complex surface with a cscK metric which M admits a radial Kahler potential. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free