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Original Articles

A Note on Del Pezzo Fibrations of Degree 1

Pages 5755-5768 | Received 01 Mar 2002, Published online: 01 Feb 2007

References

  • Artin , M. 1966 . On isolated rational singularities of surfaces . Amer. J. Math. , 88 : 129 – 136 .
  • Corti , A. 1995 . Factoring birational maps of threefolds after Sarkisov . J. Alg. Geom. , 4 : 223 – 254 .
  • Corti , A. 1996 . Del Pezzo surfaces over Dedekind schemes . Ann. of Math.(2) , 144 ( 3 ) : 641 – 683 .
  • Demazure , M. 1980 . “ Surfaces de del Pezzo ” . In Séminaire Sur Les Singularités Des Surfaces , Lect. Notes in Math. Vol. 777 , 23 – 69 . Springer-Verlag .
  • Furushima , M. 1986 . Singular del Pezzo surfaces and analytic compactifications of 3-dimensional complex affine space ℂ3 . Nagoya Math. J. , 104 : 1 – 28 .
  • Hidaka , F. and Watanabe , K. 1981 . Normal Gorenstein surfaces with ample anti-canonical divisor . Tokyo J. Math. , 4 ( 2 ) : 319 – 330 .
  • Iskovskikh , V. A. 1996 . Factorization of birational mappings of rational surfaces from the point of view of Mori theory . Russian Math. Surveys , 51 ( 4 ) : 585 – 652 .
  • Kollár , J. 1997 . Polynomials with integral coefficients, equivalent to a given polynomial . Electron. Res. Announc. Amer. Math. Soc. , 3 : 17 – 27 . (electronic)
  • Kollár , J. and Mori , S. 1998 . Birational Geometry of Algebraic Varieties Cambridge University Press .
  • Miyanishi , M. and Zhang , D.-Q. 1988 . Gorenstein log del Pezzo surfaces of rank one . J. Algebra , 118 ( 1 ) : 63 – 84 .
  • Miyanishi , M. and Zhang , D.-Q. 1993 . Gorenstein log del Pezzo surfaces II . J. Algebra , 156 ( 1 ) : 183 – 193 .
  • Park , J. 2001 . Birational maps of del Pezzo fibrations . J. Reine Angew. Math. , 538 : 213 – 221 .
  • Prokhorov , Y. G. 2000 . Boundedness of nonbirational extremal contractions . Internt. J. Math. , 11 : 393 – 411 .
  • Reid , M. 1997 . “ Chapters on algebraic surfaces ” . In Complex Algebraic Geometry 3 – 159 . Providence, RI : Amer. Math. Soc. .
  • Shokurov , V. 1993 . 3-Folds log flips . Russian Acad. Sci. Izv. Math. , 40 ( 1 ) : 95 – 202 .
  • Urabe , T. 1983 . “ On singularities on degenerate del Pezzo surfaces of degree 1, 2 ” . In Singularities, Part 2 587 – 591 . Providence, R.I. : Amer. Math. Soc. .
  • Zhang , D.-Q. 1988 . Logarithmic del Pezzo surfaces of rank one with contractible boundaries . Osaka J. Math. , 25 ( 2 ) : 461 – 497 .

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