Geometry & Topology

A simply connected surface of general type with $p_g=0$ and $K^2=3$

Heesang Park, Jongil Park, and Dongsoo Shin

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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.

Article information

Source
Geom. Topol., Volume 13, Number 2 (2009), 743-767.

Dates
Received: 10 February 2008
Revised: 6 December 2008
Accepted: 4 December 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800216

Digital Object Identifier
doi:10.2140/gt.2009.13.743

Mathematical Reviews number (MathSciNet)
MR2469529

Zentralblatt MATH identifier
1181.14042

Subjects
Primary: 14J29: Surfaces of general type
Secondary: 14J10: Families, moduli, classification: algebraic theory 14J17: Singularities [See also 14B05, 14E15] 53D05: Symplectic manifolds, general

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

Citation

Park, Heesang; Park, Jongil; Shin, Dongsoo. A simply connected surface of general type with $p_g=0$ and $K^2=3$. Geom. Topol. 13 (2009), no. 2, 743--767. doi:10.2140/gt.2009.13.743. https://projecteuclid.org/euclid.gt/1513800216


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