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arXiv · 1506.03050

Qualitative aspects of counting real rational curves on real K3 surfaces

Viatcheslav Kharlamov·Rares Rasdeaconu
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Abstract

We study qualitative aspects of the Welschinger-like $\mathbb Z$-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.

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Viatcheslav Kharlamov, Rares Rasdeaconu. 2016-03-15. Qualitative aspects of counting real rational curves on real K3 surfaces. https://doi.org/10.2140/gt.2017.21.585

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