Autoren:	Zuo, Kang
Titel:	On the negativity of moduli spaces for polarized manifolds
Online-Publikationsdatum:	27-Jun-2022
Erscheinungsdatum:	2021
Sprache des Dokuments:	Englisch
Zusammenfassung/Abstract:	Given a log base space (Y, S), parameterizing a smooth family of complex projective varieties with semi-ample canonical line bundle, we briefly recall the construction of the deformation Higgs sheaf and the comparison map on (Y, S) made in the work by Viehweg–Zuo. While almost all hyperbolicities in the sense of complex analysis such as Brody, Kobayashi, big Picard and Viehweg hyperbolicities of the base U = Y ∖ S (under some technical assumptions) follow from the negativity of the kernel of the deformation Higgs bundle we pose a conjecture on the topological hyperbolicity on U. In order to study the rigidity problem we then introduce the notions of the length and characteristic varieties of a family f : X → Y, which provide an infinitesimal characterization of products of sub log pairs in (Y, S) and an upper bound for the number of subvarieties appearing as factors in such a product. We formulate a conjecture on a characterization of non-rigid families of canonically polarized varieties.
DDC-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7214
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Vietnam journal of mathematics 49
Seitenzahl oder Artikelnummer:	527 546
Verlag:	Springer
Verlagsort:	Singapore
Erscheinungsdatum:	2021
ISSN:	2305-2228
DOI der Originalveröffentlichung:	10.1007/s10013-021-00507-6
Enthalten in den Sammlungen:	JGU-Publikationen