Exceptional singular ℚ -homology planes

Karol Palka[1]

  • [1] University of Warsaw Institute of Mathematics ul. Banacha 2 02-097 Warsaw (Poland) Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8 00-956 Warsaw (Poland)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 2, page 745-774
  • ISSN: 0373-0956

Abstract

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We consider singular ℚ -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is ℂ 1 - or ℂ * -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type A 1 and A 2 respectively.

How to cite

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Palka, Karol. "Exceptional singular $\mathbb{Q}$-homology planes." Annales de l’institut Fourier 61.2 (2011): 745-774. <http://eudml.org/doc/219718>.

@article{Palka2011,
abstract = {We consider singular $\mathbb\{Q\}$-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is $\mathbb\{C\}^1$- or $\mathbb\{C\}^*$-ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type $A_1$ and $A_2$ respectively.},
affiliation = {University of Warsaw Institute of Mathematics ul. Banacha 2 02-097 Warsaw (Poland) Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8 00-956 Warsaw (Poland)},
author = {Palka, Karol},
journal = {Annales de l’institut Fourier},
keywords = {Acyclic surface; homology plane; exceptional Q-homology plane; rational homology plane; -fibration; -fibration},
language = {eng},
number = {2},
pages = {745-774},
publisher = {Association des Annales de l’institut Fourier},
title = {Exceptional singular $\mathbb\{Q\}$-homology planes},
url = {http://eudml.org/doc/219718},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Palka, Karol
TI - Exceptional singular $\mathbb{Q}$-homology planes
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 2
SP - 745
EP - 774
AB - We consider singular $\mathbb{Q}$-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is $\mathbb{C}^1$- or $\mathbb{C}^*$-ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type $A_1$ and $A_2$ respectively.
LA - eng
KW - Acyclic surface; homology plane; exceptional Q-homology plane; rational homology plane; -fibration; -fibration
UR - http://eudml.org/doc/219718
ER -

References

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