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In this paper we construct a new family of simply connected minimal complexsurfaces of general type with $p_g=1$, $q=0$, and $K^2=3, 4, 5, 6, 8$ using a$\mathbb{Q}$-Gorenstein smoothing theory. We also reconstruct minimal complexsurfaces of general type with $p_g=1$, $q=0$, and $K^2=1, 2$ using the samemethod.

Surfaces of general type with $p_g=1$ and $q=0$