SURFACES OF GENERAL TYPE WITH pg = 1 AND q = 0

Title & Authors
SURFACES OF GENERAL TYPE WITH pg = 1 AND q = 0
Park, Heesang; Park, Jongil; Shin, Dongsoo;

Abstract
We construct a new family of simply connected minimal complex surfaces of general type with $\small{p_g}$ = 1, $\small{q}$ = 0, and $\small{K^2}$ = 3, 4, 5, 6, 8 using a $\small{\mathbb{Q}}$-Gorenstein smoothing theory.
Keywords
$\small{\mathbb{Q}}$-Gorenstein smoothing;rational blow-down surgery;surface of general type;
Language
English
Cited by
1.
Extending symmetric determinantal quartic surfaces, Geometriae Dedicata, 2014, 172, 1, 155
2.
Spherical subcategories in algebraic geometry, Mathematische Nachrichten, 2016, 289, 11-12, 1450
3.
SMOOTHLY EMBEDDED RATIONAL HOMOLOGY BALLS, Journal of the Korean Mathematical Society, 2016, 53, 6, 1293
References
1.
W. Barth, K. Hulek, C. Peters, and A. Van de Ven, Compact Complex Surfaces, 2nd ed. Springer-Verlag, Berlin, 2004.

2.
F. Catanese, Surfaces with $K^2$=pg=1 and their period mapping, Algebraic geometry (proc. Summer Meeting, Univ. Copenhagen, Copenhagen, 1978), Lecture Notes in Math. 732 (1979), 1-29.

3.
F. Catanese and O. Debarre, Surfaces with $K^2$=2, pg=1, q=0, J. Reine Angew. Math. 395 (1989), 1-55.

4.
H. Esnault and E. Viehweg, Lectures on vanishing theorems, DMV Seminar 20, Birkhauser Verlag, Basel, 1992.

5.
H. Flenner and M. Zaidenberg, Q-acyclic surfaces and their deformations, Classification of algebraic varieties (L'Aquila, 1992), 143-208, Contemp. Math., 162, Amer. Math. Soc., Providence, RI, 1994.

6.
R. E. Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995), no. 3, 527-595.

7.
J. Keum, Y. Lee, and H. Park, Construction of surfaces of general type from elliptic surfaces via Q-Gorenstein smoothing, Math. Z. 272 (2012), no 3-4, 1243-1257.

8.
S. Kondo, Enriques surfaces with nite automorphism groups, Japan. J. Math. (N.S.) 12 (1986), no. 2, 191-282.

9.
V. Kynev, An example of a simply connected surface of general type for which the local Torelli theorem does not hold, C. R. Acad. Bulgare Sci. 30 (1977), no. 3, 323-325.

10.
Y. Lee and J. Park, A simply connected surface of general type with pg = 0 and $K^2$=2, Invent. Math. 170 (2007), no. 3, 483-505.

11.
Y. Lee, A construction of Horikawa surface via Q-Gorenstein smoothings, Math. Z. 267 (2011), no. 1-2, 15-25.

12.
B. D. Park, Exotic smooth structures on $3CP^2#n{\overline}{CP^2}$, Part II, Proc. Amer. Math. Soc. 128 (2000), no. 10, 3067-3073.

13.
J. Park, Exotic smooth structures on $3CP^#8\overline{CP^2}$, Bull. London Math. Soc. 39 (2007), no. 1, 95-102.

14.
H. Park, J. Park, and D. Shin, A simply connected surface of general type with pg = 0 and$K^2$=3, Geom. Topol. 13 (2009), no. 2, 743-767.

15.
H. Park, A simply connected surface of general type with pg = 0 and $K^2=4$, Geom. Topol. 13 (2009), no. 3, 1483-1494.

16.
A. Stipsicz and Z. Szabo, Small exotic 4-manifolds with $b^+_2$= 3, Bull. London Math. Soc. 38 (2006), no. 3, 501-506.

17.
A. Todorov, A construction of surfaces with pg = 1, q = 0 and $2{\leq}(K^2){\leq}8$ : Counterexamples of the global Torelli theorem, Invent. Math. 63 (1981), no. 2, 287-304.