Complements of hyperplane sub-bundles in projective spaces bundles over \({\mathbb {P}}^{1}\)

详细信息    查看全文

• 作者：Adrien Dubouloz (1)
  
  1. CNRS ; Institut de Math茅matiques de Bourgogne ; Universit茅 de Bourgogne ; 9 Avenue Alain Savary ; BP 47870 ; 21078聽 ; Dijon Cedex ; France
  
• 关键词：14L30 ; 14R05 ; 14R25
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：361
• 期：1-2
• 页码：259-273
• 全文大小：255 KB
• 参考文献：1. Dubouloz, A.: Danielewski鈥揊ieseler surfaces. Transform. Groups 10(2), 139鈥?62 (2005) 31-005-1004-x" target="_blank" title="It opens in new window">CrossRef
  2. Dubouloz, A., Finston, D.: On exotic affine 3-spheres. J. Algebr. Geom. 23, 445鈥?69 (2014) 3911-2014-00612-3" target="_blank" title="It opens in new window">CrossRef
  3. Fieseler, K.-H.: On complex affine surfaces with \({\mathbb{C}}^+\) -action. Comment. Math. Helv. 69(1), 5鈥?7 (1994) CrossRef
  4. Flenner, H., Kaliman, S., Zaidenberg, M.: On the Danilov鈥揋izatullin isomorphism theorem. L鈥橢nseignement Mathmatique 55(2), 1鈥? (2009)
  5. Gizatullin, M.H., Danilov, V.I.: Automorphisms of affine surfaces II. Izv. Akad. Nauk SSSR Ser. Mat. 41(1), 54鈥?03 (1977)
  6. Grothendieck, A.: Sur la classification des fibr茅s holomorphes sur la sph猫re de Riemann. Am. J. Math. 79(1), 121鈥?38 (1957) 307/2372388" target="_blank" title="It opens in new window">CrossRef
  7. Grothendieck, A., Dieudonn茅, J.: EGA IV.脡tude locale des sch茅mas et des morphismes de sch茅mas, Quatri猫me partie. Publications Math茅matiques de I鈥橧H脡S, 32, 5鈥?61 (1967)
  8. Miyanishi, M.: Open Algebraic Surfaces. Amer. Math. Soc. 12. CRM Monograph Series, Providence (2001)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle \(H\) of a \({\mathbb {P}}^{r-1}\) -bundle \({\mathbb {P}}(E)\rightarrow {\mathbb {P}}^{1}\) depends only on the \(r\) -fold self-intersection \((H^{r})\in {\mathbb {Z}}\) of \(H\) . In particular it depends neither on the ambient bundle \({\mathbb {P}}(E)\) nor on the choice of a particular ample sub-bundle with given \(r\) -fold self-intersection. The proof exploits the unexpected property that every such complement comes equipped with the additional structure of an affine-linear bundle over the affine line with a double origin.