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Birational Geometry of 3-fold Mori Fibre Spaces

By Gavin D. Brown, Alessio Corti and Francesco Zucconi

Abstract

We study the geography and birational geometry of 3-fold conic bundles over P^2 and cubic del Pezzo fibrations over P^1. We discuss many explicit examples and raise several open questions

Topics: QA
Year: 2005
OAI identifier: oai:kar.kent.ac.uk:729

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Citations

  1. (1995). Algebra i Algebr. Geom.):128–138,
  2. (1981). Babbage’s conjecture, contact of surfaces, symmetric determinantal varieties and applications. doi
  3. (2002). Birational automorphisms of a class of varieties fibered by cubic surfaces. doi
  4. (1980). Birational automorphisms of conic bundles. doi
  5. (1996). Birational automorphisms of multidimensional algebraic manifolds. doi
  6. (1997). Birational automorphisms of three-dimensional algebraic manifolds stratified on cubic surfaces. doi
  7. (1998). Birational automorphisms of three-dimensional algebraic varieties fibered by Del Pezzo surfaces. doi
  8. (1979). Birational automorphisms of three-dimensional algebraic varieties representable as a conic bundle. doi
  9. (1998). Birational automorphisms of three-dimensional algebraic varieties with a pencil of del Pezzo surfaces. doi
  10. Birational geometry of terminal quartic 3-folds. doi
  11. Birational geometry of terminal quartic 3-folds. I. to appear in doi
  12. Birational models of del Pezzo fibrations. doi
  13. (2000). Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. doi
  14. (2000). Boundedness of canonical Q-Fano 3-folds. doi
  15. (1993). Chapters on algebraic surfaces. doi
  16. (2000). Dedicated to William Fulton on the occasion of his 60th birthday. doi
  17. (1996). Del Pezzo surfaces over Dedekind schemes. doi
  18. (2000). Essentials of the method of maximal singularities. doi
  19. (1995). Factoring birational maps of threefolds after
  20. (2000). Fano 3-fold hypersurfaces. doi
  21. (2002). Fano 3-folds, K3 surfaces and graded rings. doi
  22. (1999). Flips arising as quotients of hypersurfaces. doi
  23. (2000). Graded rings and birational geometry. doi
  24. (1998). Graded rings corresponding to polarised K3 surfaces and Q-Fano 3-folds. PhD thesis,
  25. (2000). Mori dream spaces doi
  26. Non-rationality of a three-dimensional Fano variety of index 2 and degree 1.
  27. (1902). Note on the reduction of a ternary quantic to a symmetric determinantal.
  28. (1996). On a rationality criterion for conic bundles. doi
  29. On a rigidity criterion for del Pezzo fibrations over P1.
  30. (2002). On classification of Q-Fano 3-folds of Gorenstein index
  31. On conic bundle structures. doi
  32. (2001). On fiberwise surgeries of fibrations on a del Pezzo surface of degree 2. Uspekhi Mat.
  33. (2001). On fibrations into del Pezzo surfaces. doi
  34. (2000). On the birational rigidity of some pencils of del Pezzo surfaces. doi
  35. (1987). On the rationality problem for conic bundles. doi
  36. (1991). On the rationality problem for three-dimensional algebraic varieties fibered over del Pezzo surfaces.
  37. (1995). On the rationality problem for three-dimensional algebraic varieties fibered over del Pezzo surfaces. Trudy Mat.
  38. (1997). Polynomials with integral coefficients, equivalent to a given polynomial.
  39. (2003). Rational and nearly rational varieties. doi
  40. (2000). Singularities of linear systems and 3-fold birational geometry. doi
  41. (1972). Some elementary examples of unirational varieties which are not rational. doi
  42. (1999). The graded ring of a rank 2 Sarkisov link. In preparation.
  43. (1989). Towards the problem of rationality of conic bundles. doi

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