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Qualitative aspects of
counting real rational curves on real K3 surfaces
Viatcheslav Kharlamov and Rareş Răsdeaconu |
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Geometry & Topology 21 (2017) 585–601
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 14N99
Secondary: 14P99, 14J28
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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
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Authors |
| Viatcheslav Kharlamov | |
| IRMA UMR 7501 Université de Strasbourg 7 Rue René-Descartes 67084 Strasbourg Cedex France |
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| Rareş Răsdeaconu | |
| Department of Mathematics Vanderbilt University 1326 Stevenson Center Nashville, TN 37240 United States |
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