seminar: An analogue of Shafarevich hyperbolicity for families over higher-dimensional base manifolds

speaker: Stefan Kebekus (Universität zu Köln, Germany)

abstract: 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 threefold Y 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 Y: in all relevant cases the minimal model program leads to a fiber space whose fibration factors the moduli map. A much refined affirmative answer to Viehweg's conjecture for families over threefolds follows as a corollary. For families over surfaces, the moduli map can be often be described quite explicitly.

timetable:
Mon 23 Jun, 17:00 - 18:00, Aula Dini
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