DOI QR코드

DOI QR Code

SMOOTHLY EMBEDDED RATIONAL HOMOLOGY BALLS

  • Park, Heesang (Department of Mathematics Konkuk University) ;
  • Park, Jongil (Department of Mathematical Sciences Seoul National University) ;
  • Shin, Dongsoo (Department of Mathematics Chungnam National University)
  • Received : 2015.08.15
  • Published : 2016.11.01

Abstract

In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth 2-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.

Keywords

References

  1. A. Casson and J. Harer, Some homology lens spaces which bound rational homology balls, Pacific J. Math. 96 (1981), no. 1, 23-36. https://doi.org/10.2140/pjm.1981.96.23
  2. R. Fintushel and R. Stern, Rational blowdowns of smooth 4-manifolds, J. Differential Geom. 46 (1997), no. 2, 181-235. https://doi.org/10.4310/jdg/1214459932
  3. P. Hacking, J. Tevelev, and G. Urzua, Flipping surfaces, arXiv:1310.1580, to appear in J. Algebraic Geom.
  4. T. Khodorovskiy, Smooth embeddings of rational homology balls, Topology Appl. 161 (2014), 386-396. https://doi.org/10.1016/j.topol.2013.10.039
  5. J. Kollar and S. Mori, Classification of three-dimensional ips, J. Amer. Math. Soc. 5 (1992), no. 3, 533-703. https://doi.org/10.1090/S0894-0347-1992-1149195-9
  6. J. Kollar and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299-338. https://doi.org/10.1007/BF01389370
  7. Y. Lee and J. Park, A simply connected surface of general type with $p_g$ = 0 and $K^2$ = 2, Invent. Math. 170 (2007), 483-505. https://doi.org/10.1007/s00222-007-0069-7
  8. Y. Lee and J. Park, A complex surface of general type with $p_g$ = 0, $K^2$ = 2 and $H_1$ = ${\mathbb{Z}/2{\mathbb{Z}}$, Math. Res. Lett. 16 (2009), 323-330. https://doi.org/10.4310/MRL.2009.v16.n2.a9
  9. H. Park, J. Park, and D. Shin, A simply connected surface of general type with $p_g$ = 0 and $K^2$ = 3, Geom. Topol. 13 (2009), no. 2, 743-767. https://doi.org/10.2140/gt.2009.13.743
  10. H. Park, J. Park, and D. Shin, A simply connected surface of general type with $p_g$ = 0 and $K^2$ = 4, Geom. Topol. 13 (2009), no. 3, 1483-1494. https://doi.org/10.2140/gt.2009.13.1483
  11. H. Park, J. Park, and D. Shin, A complex surface of general type with $p_g$ = 0, $K^2$ = 2 and $H_1$ = ${\mathbb{Z}/4{\mathbb{Z}}$, Trans. Amer. Math. Soc. 365 (2013), no. 11, 5713-5736. https://doi.org/10.1090/S0002-9947-2013-05696-6
  12. H. Park, J. Park, and D. Shin, Surfaces of general type with $p_g$ = 1 and q = 0, J. Korean Math. Soc. 50 (2013), no. 3, 493-507. https://doi.org/10.4134/JKMS.2013.50.3.493
  13. H. Park, D. Shin, and G. Urzua, A simply connected numerical Campedelli surface with an involution, Math. Ann. 357 (2013), no. 1, 31-49. https://doi.org/10.1007/s00208-013-0905-6
  14. J. Park, Seiberg-Witten invariants of generalised rational blow-downs, Bull. Austral. Math. Soc. 56 (1997), no. 3, 363-384. https://doi.org/10.1017/S0004972700031154
  15. J. Park, Simply connected symplectic 4-manifolds with $b_2^+$ = 1 and $c_1^2$ = 2, Invent. Math. 159 (2005), no. 3, 657-667. https://doi.org/10.1007/s00222-004-0404-1
  16. J. Park, A. Stipsicz, and Z. Szabo, Exotic smooth structures on ${\mathbb{C}P^2}$#5 $\overline{\mathbb{CP}^2}$, Math. Res. Lett. 12 (2005), no. 5-6, 701-712. https://doi.org/10.4310/MRL.2005.v12.n5.a7
  17. O. Riemenschneider, Deformationen von Quotientensingularitaten (nach zyklischen Gruppen), Math. Ann. 209 (1974), 211-248. https://doi.org/10.1007/BF01351850
  18. A. Stipsicz and Z. Szabo, An exotic smooth structure on ${\mathbb{CP}^2}$ #6 $\overline{\mathbb{CP}^2}$, Geom. Topol. 9 (2005), 813-832. https://doi.org/10.2140/gt.2005.9.813
  19. G. Urzua, Identifying neighbors of stable surfaces, to appear in The Annali della Scuola Normale Superiore di Pisa (DOI Number: 10.2422/2036-2145.201311002).
  20. J. Wahl, Equisingular deformations of normal surface singularities. I, Ann. of Math. (2) 104 (1976), no. 2, 325-356. https://doi.org/10.2307/1971049
  21. J. Wahl, Smoothing of normal surface singularities, Topology 20 (1981), no. 3, 219-246. https://doi.org/10.1016/0040-9383(81)90001-X