A simply connected surface of general type with pg = 0 and K2 = 3

Park, Heesang; Park, Jongil; Shin, Dongsoo

doi:10.2140/gt.2009.13.743

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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

DOI: 10.2140/gt.2009.13.743

Correction: 10.2140/gt.2011.15.499

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 $p_{g} = 0$ and $K^{2} = 3$ using a rational blow-down surgery and $ℚ$ –Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic $4$ –manifold with $b_{2}^{+} = 1$ and $K^{2} = 4$ .

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

Correction: 25 March 2011

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

Volume 13, issue 2 (2009)