Vol. 14, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Positivity results for spaces of rational curves

Roya Beheshti and Eric Riedl

Vol. 14 (2020), No. 2, 485–500
Abstract

Let X be a very general hypersurface of degree d in Pn. We investigate positivity properties of the spaces Re(X) of degree e rational curves in X. We show that for small e, Re(X) has no rational curves meeting the locus of smooth embedded curves. We show that for n d, there are no rational curves other than lines in the locus Y X swept out by lines. We exhibit differential forms on a smooth compactification of Re(X) for every e and n 2 d 1 2(n + 1).

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.236.212.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
hypersurface, rational curve, rational surface, birational geometry
Mathematical Subject Classification 2010
Primary: 14E08
Milestones
Received: 30 April 2019
Revised: 14 August 2019
Accepted: 16 September 2019
Published: 29 May 2020
Authors
Roya Beheshti
Mathematics and Statistics
Washington University in St. Louis
Saint Louis, MO
United States
Eric Riedl
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States