Volume 13, issue 2 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A simply connected surface of general type with $p_g=0$ and $K^2=3$

Heesang Park, Jongil Park and Dongsoo Shin

Geometry & Topology 13 (2009) 743–767

Erratum: Geometry & Topology 15 (2011) 499–500

Abstract

Motivated by a recent result of Y Lee and the second author [Invent. Math. 170 (2007) 483-505], we construct a simply connected minimal complex surface of general type with pg = 0 and K2 = 3 using a rational blow-down surgery and –Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4–manifold with b2+ = 1 and K2 = 4.

Keywords
$\mathbb{Q}$-Gorenstein smoothing, rational blow-down, surface of general type
Mathematical Subject Classification 2000
Primary: 14J29
Secondary: 14J10, 14J17, 53D05
References
Publication
Received: 10 February 2008
Revised: 6 December 2008
Accepted: 4 December 2008
Published: 5 January 2009
Proposed: Ron Stern
Seconded: Ron Fintushel, Simon Donaldson
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