𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Connections between the geometry of a projective variety and of an ample section

✍ Scribed by Marco Andreatta; Carla Novelli; Gianluca Occhetta

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
164 KB
Volume
279
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let X be a smooth complex projective variety and let Z =(s =0) be a smooth submanifold which is the zero locus of a section of an ample vector bundle E of rank r with dim Z =dim X –r.

We show with some examples that in general the Kleiman–Mori cones NE(Z) and NE(X) are different. We then give a necessary and sufficient condition for an extremal ray in NE(X) to be also extremal in NE(Z).

We apply this result to the case r =1 and Z a Fano manifold of high index;in particular we classify all X with an ample divisor which is a Mukai manifold of dimension β‰₯4.

In the last section we prove a general result in case Z is a minimal variety with 0 ≀κ (Z) Z. (Β© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Formation of a Constrained-Geometry Zieg
Formation of a Constrained-Geometry Ziegler Catalyst System Containing a C1 Instead of the Usual Si1 Connection Between the Cyclopentadienyl and Amido Ligand Components
✍ Lothar Duda; Gerhard Erker; Roland FrΓΆhlich; Frank Zippel πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 426 KB πŸ‘ 1 views

6-Amino-6-methylfulvene (4) is cleanly N-acylated by formation of [(C 5 H 4 )C(=CH 2 )NCOCMe 3 ]Zr(NEt 2 ) 2 (11) (70 % isolated), and the reaction of 8b with (Et 2 N) 2 ZrCl 2 yields treatment with pivaloylchloride/triethylamine to give the fulvene (C 5 H 4 )=C(CH 3 )NHCOCMe 3 (5c). Treatment of 4