Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks

2002/10/20 by Eckart Viehweg, Kang Zuo, Viehweg, Eckart +1
Mathematics · #14D06 (Primary) 14D22 #14E30 (Secondary) #14J15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D06 #msc:14D22 #msc:14E30 #msc:14J15

paper · pdf · doi:10.48550/arxiv.math/0210310

26 pages, AMSLaTeX, 3nd version with some minor corrections and a new introduction

arxiv created 2003/03/08 · arxiv updated 2009/11/30

Abstract

We extend some of the results obtained for subvarieties of the moduli stack of canonically polarized manifolds in "Base spaces of non-isotrivial families of smooth minimal models" (math.AG/0103122) to moduli of polarized minimal models of Kodaira dimension zero. To this aim we first show that for those manifolds there are no non isotrivial families of minimal models, which are birationally isotrivial. In the last chapter, we discuss the rigidity of curves in the moduli stack of canonically polarized manifolds and of polarized minimal models of Kodaira dimension zero.

Related

• Birational geometry of smooth families of varieties admitting good minimal models
• Base spaces of non-isotrivial families of smooth minimal models
• Moduli of algebraic varieties
• Compactifications of smooth families and of moduli spaces of polarized manifolds
• On the distribution of non-rigid families in the moduli spaces