The structure of surfaces mapping to the moduli stack of canonically polarized varieties

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is necessarily of log general type. Given a quasi-projective surface that maps to the moduli stack, we employ extension properties of logarithmic pluri-forms to establish a strong relationship between the moduli map and the minimal model program of the surface. As a result, we can describe the fibration induced by the moduli map quite explicitly. A refined affirmative answer to Viehweg's conjecture for families over surfaces follows as a corollary.
19 pages

Keywords

Algebraic Geometry, 14D20, 14D06

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/134155

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0707.2054
 http://arxiv.org/abs/0707.2054

Collections

arXiv