A complex surface of general type with 𝑝_{𝑔}=0, 𝐾²=2 and 𝐻₁=ℤ/4ℤ

Park, Heesang; Park, Jongil; Shin, Dongsoo

doi:10.1090/S0002-9947-2013-05696-6

A complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb {Z}/4\mathbb {Z}$
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by Heesang Park, Jongil Park and Dongsoo Shin PDF

Trans. Amer. Math. Soc. 365 (2013), 5713-5736 Request permission

Abstract:

We construct a new minimal complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb {Z}/4\mathbb {Z}$ (in fact, $\pi _1^{\text {alg}}=\mathbb {Z}/4\mathbb {Z}$), which settles the existence question for numerical Campedelli surfaces with all possible algebraic fundamental groups. The main techniques involved in the construction are a rational blow-down surgery and a $\mathbb {Q}$-Gorenstein smoothing theory.

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