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On Semistable Mori Conic Bundles

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We study Fano-Mori contractions from threefolds to surfaces satisfying the semistability assumption. A number of examples are constructed.

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REFERENCES

  1. E. Looijenga and J. Wahl, “Quadratic functions and smoothing surface singularities,” Topology, 25, 261–291 (1986).

    Article  Google Scholar 

  2. J. Kollar and S. Mori, “Classification of three-dimensional flips,” J. Amer. Math. Soc., 5, 533–703 (1992).

    Google Scholar 

  3. J. Kollar and S. Mori, Birational Geometry of Algebraic Varieties, Cambridge Tracts Math., 134, Cambridge Univ. Press, Cambridge (1998).

    Google Scholar 

  4. J. Kollar and N. I. Shepherd-Barron, “Threefolds and deformations of surface singularities,” Invent. Math., 91, 299–338, (1988).

    Article  Google Scholar 

  5. J. Kollar et al., “Flips and abundance for algebraic threefolds,” in: Summer Seminar at the Univ. of Utah, Salt Lake City, 1991, Asterisque, 211 (1992).

  6. Yu. G. Prokhorov, “On the existence of complements of the canonical divisor for Mori conic bundles,” Russ. Acad. Sci. Sb. Math., 188, 1665–1685 (1997).

    Google Scholar 

  7. Yu. G. Prokhorov, “Mori conic bundles with a reduced log terminal boundary,” J. Math. Sci., 94, 1051–1059 (1999).

    Google Scholar 

  8. Yu. G. Prokhorov, “On semistable Mori contractions,” e-print math.AG/0305190; to appear in Izv. Math. Russ. Acad. Sci., No. 2 (2004).

  9. V. V. Shokurov, “Semistable 3-fold flips,” Russ. Acad. Sci. Izv., Math., 42, 371–425 (1994).

    Google Scholar 

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra, 2004.

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Prokhorov, Y.G. On Semistable Mori Conic Bundles. J Math Sci 131, 6140–6147 (2005). https://doi.org/10.1007/s10958-005-0467-6

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  • DOI: https://doi.org/10.1007/s10958-005-0467-6

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