#### Volume 21, issue 1 (2017)

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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 $ℤ$–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