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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(3): 493-507

Printed May 1, 2013

https://doi.org/10.4134/JKMS.2013.50.3.493

Copyright © The Korean Mathematical Society.

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

Heesang Park, Jongil Park, and Dongsoo Shin

Korea Institute for Advanced Study, Korea Institute for Advanced Study, Korea Institute for Advanced Study

Abstract

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We construct a new family of simply connected minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=3, 4, 5, 6, 8$ using a $\mathbb{Q}$-Gorenstein smoothing theory.

Keywords: $\mathbb{Q}$-Gorenstein smoothing, rational blow-down surgery, surface of general type

MSC numbers: Primary 14J29; Secondary 14J10, 14J17, 53D05

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