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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
Bibliography
1 A Akhmedov, Small exotic $4$–manifolds arXiv:math.GT/0612130
2 M Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962) 485 MR0146182
3 S Baldridge, P Kirk, Constructions of small symplectic $4$–manifolds using Luttinger surgery arXiv:math.GT/0703065
4 R Barlow, A simply connected surface of general type with $p_g=0$, Invent. Math. 79 (1985) 293 MR778128
5 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, Ergebnisse series 3: Modern Surveys in Math. 4, Springer (2004) MR2030225
6 R Fintushel, R J Stern, Rational blowdowns of smooth $4$–manifolds, J. Differential Geom. 46 (1997) 181 MR1484044
7 H Flenner, M Zaidenberg, $\mathbf Q$–acyclic surfaces and their deformations, from: "Classification of algebraic varieties (L'Aquila, 1992)" (editors C Ciliberto, E L Livorni, A J Sommese), Contemp. Math. 162, Amer. Math. Soc. (1994) 143 MR1272698
8 J Kollár, N I Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988) 299 MR922803
9 Y Lee, J Park, A simply connected surface of general type with $p_g=0$ and $K^2=2$, Invent. Math. 170 (2007) 483 MR2357500
10 S Lichtenbaum, M Schlessinger, The cotangent complex of a morphism, Trans. Amer. Math. Soc. 128 (1967) 41 MR0209339
11 E Looijenga, J Wahl, Quadratic functions and smoothing surface singularities, Topology 25 (1986) 261 MR842425
12 M Manetti, Normal degenerations of the complex projective plane, J. Reine Angew. Math. 419 (1991) 89 MR1116920
13 D Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes Études Sci. Publ. Math. (1961) 5 MR0153682
14 N Nakayama, Zariski-decomposition and abundance, MSJ Memoirs 14, Math. Soc. of Japan (2004) MR2104208
15 P Ozsváth, Z Szabó, On Park's exotic smooth four-manifolds, from: "Geometry and topology of manifolds" (editors H U Boden, I Hambleton, A J Nicas, B D Park), Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 253 MR2189937
16 V P Palamodov, Deformations of complex spaces, Uspehi Mat. Nauk 31 (1976) 129 MR0508121
17 J Park, Seiberg–Witten invariants of generalised rational blow-downs, Bull. Austral. Math. Soc. 56 (1997) 363 MR1490654
18 J Park, Simply connected symplectic $4$–manifolds with $b^+_2=1$ and $c^2_1=2$, Invent. Math. 159 (2005) 657 MR2125736
19 U Persson, Configurations of Kodaira fibers on rational elliptic surfaces, Math. Z. 205 (1990) 1 MR1069483
20 A I Stipsicz, Z Szabó, An exotic smooth structure on $\mathbb C\mathbb P^2\#6\overline\mathbb{C\mathbb P^2}$, Geom. Topol. 9 (2005) 813 MR2140993
21 M Symington, Symplectic rational blowdowns, J. Differential Geom. 50 (1998) 505 MR1690738
22 M Symington, Generalized symplectic rational blowdowns, Algebr. Geom. Topol. 1 (2001) 503 MR1852770
23 J Wahl, Elliptic deformations of minimally elliptic singularities, Math. Ann. 253 (1980) 241 MR597833
24 J Wahl, Smoothings of normal surface singularities, Topology 20 (1981) 219 MR608599