Finite TYCZ expansions and cscK metrics

Autor(es)

Loi, Andrea ^[1] ; Mossa, Roberto ^[2] ; Zuddas, Fabio ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 484, n. 1 APR 1 2020.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 18/08971-9 - Entropia diastática e rigidez das variedades hiperbólicas
• Beneficiário: Roberto Mossa
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores