Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-10-31T23:14:40.105Z Has data issue: false hasContentIssue false

Threefolds of degree 11 in P5

Published online by Cambridge University Press:  06 July 2010

G. Ellingsrud
Affiliation:
Universitetet i Bergen, Norway
C. Peskine
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
G. Sacchiero
Affiliation:
Università degli Studi di Trieste
S. A. Stromme
Affiliation:
Universitetet i Bergen, Norway
Get access

Summary

Introduction. This article is devoted to the classification of smooth projective threefolds in P5.

In [BSS] we classified degree 9 and 10 threefolds in P5; the lower degree varieties had already been classified (see [11], [12], [13], [O1], [O2]). In that article, we used known constraints and new results from adjunction theory ([BBS], [S1], [S5], [SV]) to restrict the possible invariants. We then used liaison to construct examples with the possible invariants. Uniqueness of the examples satisfying the invariants was also shown.

In this paper we extend the methods of [BSS] to deal with the degree 11 case. The list we obtain of the possible invariants is again short, and we have examples for every possible set of invariants. We refer the reader to the start of § 4 where there is a table giving the degree 11 classification. For the reader's convenience we have given a one page appendix to this paper with a table giving the known classification of degree ≤ 10 threefolds in P5.

Degree 11 is especially interesting because our calculations show that the number of possible sets of invariants begins to increase quite fast from degree 12 on. This is discussed in (4.6).

We would like to thank the DFG-Schwerpunktprogram “Komplexe Mannigfaltigkeiten” for making it possible for us to work together at the University of Bayreuth in the summer of 1988. The third author would like to thank the National Science Foundation (DMS 87-22330 and DMS 89-21702). The first and the third author would like to thank the University of Notre Dame for its support. We would like to thank Ms. Cinzia Matrl for the excellent typing.

Type
Chapter
Information
Complex Projective Geometry
Selected Papers
, pp. 59 - 80
Publisher: Cambridge University Press
Print publication year: 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×