Surfaces of general type with K-2=2 chi-1
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Werner 2015 Kyoto preprint.pdf
We classify minimal algebraic surfaces of general type having K2=2χ−1 and χ≥7. Such surfaces are regular with canonical map of degree one or two. If pg≥13, then the surface is a genus-two fibration; otherwise we use the canonical map to describe these surfaces as birational either to the canonical image or to a double cover of a rational surface.
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