Volume 21, issue 1 (2017)

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

Volume 21
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Qualitative aspects of counting real rational curves on real K3 surfaces

Viatcheslav Kharlamov and Rareş Răsdeaconu

Geometry & Topology 21 (2017) 585–601
Abstract

We study qualitative aspects of the Welschinger-like –valued count of real rational curves on primitively polarized real K3 surfaces. In particular, we prove that, with respect to the degree of the polarization, at logarithmic scale, the rate of growth of the number of such real rational curves is, up to a constant factor, the rate of growth of the number of complex rational curves. We indicate a few instances when the lower bound for the number of real rational curves provided by our count is sharp. In addition, we exhibit various congruences between real and complex counts.

Keywords
$K3$ surfaces, real rational curves, Yau–Zaslow formula, Welschinger invariants
Mathematical Subject Classification 2010
Primary: 14N99
Secondary: 14P99, 14J28
References
Publication
Received: 9 June 2015
Revised: 26 January 2016
Accepted: 12 March 2016
Published: 10 February 2017
Proposed: Lothar Göttsche
Seconded: Gang Tian, Yasha Eliashberg
Authors
Viatcheslav Kharlamov
IRMA UMR 7501
Université de Strasbourg
7 Rue René-Descartes
67084 Strasbourg Cedex
France
Rareş Răsdeaconu
Department of Mathematics
Vanderbilt University
1326 Stevenson Center
Nashville, TN 37240
United States