Volume 13, issue 3 (2009)

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ISSN (electronic): 1364-0380
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A simply connected surface of general type with $p_g=0$ and $K^2=4$

Heesang Park, Jongil Park and Dongsoo Shin

Geometry & Topology 13 (2009) 1483–1494
Abstract

As a continuation of the recent results of Y Lee and the second author [Invent. Math. 170 (2007) 483-505] and the authors [Geom. Topol. 13 (2009) 743-767], we construct a simply connected minimal complex surface of general type with pg = 0 and K2 = 4 by using a rational blow-down surgery and –Gorenstein smoothing theory.

Keywords
rational blow-down, $\mathbb{Q}$–Gorenstein smoothing, surface of general type
Mathematical Subject Classification 2000
Primary: 14J29
Secondary: 14J10, 14J17, 53D05
References
Publication
Received: 6 December 2008
Accepted: 10 February 2009
Published: 24 February 2009
Proposed: Ron Stern
Seconded: Jim Bryan, Ron Fintushel
Authors
Heesang Park
Department of Mathematical Sciences
Seoul National University
San 56-1, Sillim-dong, Gwanak-gu
Seoul 151-747
Korea
Jongil Park
Department of Mathematical Sciences
Seoul National University
San 56-1, Sillim-dong, Gwanak-gu
Seoul 151-747
Korea
Dongsoo Shin
Department of Mathematics
Pohang University of Science and Technology
San 31, Hyoja-dong, Nam-gu
Pohang, Gyungbuk 790-784
Korea