Compactifications of smooth families and of moduli spaces of polarized manifolds
| dc.creator | Viehweg, Eckart | |
| dc.date | 2006-05-03 | |
| dc.date | 2008-05-07 | |
| dc.date.accessioned | 2026-07-07T09:37:21Z | |
| dc.date.available | 2026-07-07T09:37:21Z | |
| dc.description | Let M be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for a given finite set I of natural numbers m>1 with h(m)>0 a projective compactification M' of the reduced scheme underlying M such that the ample invertible sheaf L corresponding to the determinant of the direct image of the m-th power of the relative dualizing sheaf on the moduli stack, has a natural extension L' to M'. A similar result is shown for moduli of polarized minimal models of Kodaira dimension zero. In both cases "natural" means that the pullback of L' to a curve C --> M', induced by a family f:X --> C is isomorphic to the determinant of the direct image of the m-th power of the relative dualizing sheaf whenever f is birational to a semi-stable family. Besides of the weak semistable reduction of Abramovich-Karu and the extension theorem of Gabber there are new tools, hopefully of interest by itself. In particular we will need a theorem on the flattening of multiplier sheaves in families, on their compatibility with pullbacks and on base change for their direct images, twisted by certain semiample sheaves. Following suggestions of a referee, we reorganized the article, we added several comments explaining the main line of the proof, and we changed notations a little bit. | |
| dc.description | Revised version, AMSLaTeX, 88 pages. The article was partly reformulated and reorganized | |
| dc.identifier | https://arxiv.org/abs/math/0605093 | |
| dc.identifier | http://arxiv.org/abs/math/0605093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160433 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J10 (Primary); 14D22, 14E99, 14D06 (Secondary) | |
| dc.title | Compactifications of smooth families and of moduli spaces of polarized manifolds | |
| dc.type | text |