Geodesic
A simply connected surface of general type with pg = 0 and K2 = 4
Park, Heesang1 ; Park, Jongil1 ; Shin, Dongsoo2
1 Department of Mathematical Sciences, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, Korea
2 Department of Mathematics, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Gyungbuk 790-784, Korea
Geometry & topology, Tome 13 (2009) no. 3, pp. 1483-1494.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 ℚ–Gorenstein smoothing theory.

DOI : 10.2140/gt.2009.13.1483
Keywords: rational blow-down, $\mathbb{Q}$–Gorenstein smoothing, surface of general type

Park, Heesang 1 ; Park, Jongil 1 ; Shin, Dongsoo 2

1 Department of Mathematical Sciences, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, Korea
2 Department of Mathematics, Pohang University of Science and Technology, San 31, Hyoja-dong, Nam-gu, Pohang, Gyungbuk 790-784, Korea 
@article{GT_2009_13_3_a5,
     author = {Park, Heesang and Park, Jongil and Shin, Dongsoo},
     title = {A simply connected surface of general type with pg = 0 and {K2} = 4},
     journal = {Geometry & topology},
     pages = {1483--1494},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2009},
     doi = {10.2140/gt.2009.13.1483},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.1483/}
}
TY  - JOUR
AU  - Park, Heesang
AU  - Park, Jongil
AU  - Shin, Dongsoo
TI  - A simply connected surface of general type with pg = 0 and K2 = 4
JO  - Geometry & topology
PY  - 2009
SP  - 1483
EP  - 1494
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.1483/
DO  - 10.2140/gt.2009.13.1483
ID  - GT_2009_13_3_a5
ER  - 
%0 Journal Article
%A Park, Heesang
%A Park, Jongil
%A Shin, Dongsoo
%T A simply connected surface of general type with pg = 0 and K2 = 4
%J Geometry & topology
%D 2009
%P 1483-1494
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.1483/
%R 10.2140/gt.2009.13.1483
%F GT_2009_13_3_a5
Park, Heesang; Park, Jongil; Shin, Dongsoo. A simply connected surface of general type with pg = 0 and K2 = 4. Geometry & topology, Tome 13 (2009) no. 3, pp. 1483-1494. doi : 10.2140/gt.2009.13.1483. http://geodesic.mathdoc.fr/articles/10.2140/gt.2009.13.1483/

[1] T Aubin, Équations du type Monge-Ampère sur les variétés kähleriennes compactes, C. R. Acad. Sci. Paris Sér. A-B 283 (1976)

[2] R Barlow, A simply connected surface of general type with $p_g=0$, Invent. Math. 79 (1985) 293

[3] W P Barth, K Hulek, C A M Peters, A Van De Ven, Compact complex surfaces, Ergebnisse der Math. und ihrer Grenzgebiete. 3. Folge. A Ser. of Modern Surveys in Math. 4, Springer (2004)

[4] J Kollár, S Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math. 134, Cambridge Univ. Press (1998)

[5] Y Lee, J Park, A simply connected surface of general type with $p_g=0$ and $K^2=2$, Invent. Math. 170 (2007) 483

[6] H Park, J Park, D Shin, A simply connected surface of general type with $p_g=0$ and $K^2=3$, Geom. Topol. 13 (2009) 743

[7] J Park, Simply connected symplectic $4$–manifolds with $b^+_2=1$ and $c^2_1=2$, Invent. Math. 159 (2005) 657

[8] U Persson, Configurations of Kodaira fibers on rational elliptic surfaces, Math. Z. 205 (1990) 1

[9] R Răsdeaconu, I Şuvaina, Smooth structures and Einstein metrics on $\mathbb{CP}^2 \# 5, 6, 7\overline{\mathbb{CP}^2}$

[10] S T Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A. 74 (1977) 1798

Cité par Sources :