# Rational configurations in K3 surfaces and simply-connected $p_g=1$ surfaces for $K^2=1,2,3,4,5,6,7,8,9$

@inproceedings{Reyes2021RationalCI, title={Rational configurations in K3 surfaces and simply-connected \$p\_g=1\$ surfaces for \$K^2=1,2,3,4,5,6,7,8,9\$}, author={Javier Reyes and Giancarlo Urz'ua}, year={2021} }

We prove the existence of (20 − 2K)-dimensional families of simply-connected surfaces with ample canonical class, pg = 1, and 1 ≤ K ≤ 9, and we study the relation with configurations of rational curves in K3 surfaces via Q-Gorenstein smoothings. Our surfaces with K = 7 and K = 9 are the first surfaces known in the literature, together with the existence of a 4dimensional family for K = 8.

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