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2 results

  • Derived categories and rationality of conic bundles

  • Part of
  • Marcello Bernardara, Michele Bolognesi
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 11 / November 2013
    Published online by Cambridge University Press:
    07 October 2013, pp. 1789-1817
    Print publication:
    November 2013
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  • We show that a standard conic bundle over a minimal rational surface is rational and its Jacobian splits as the direct sum of Jacobians of curves if and only if its derived category admits a semiorthogonal decomposition by exceptional objects and the derived categories of those curves. Moreover, such a decomposition gives the splitting of the intermediate Jacobian also when the surface is not minimal.

  • On the classification of crepant analytically extremal contractions of smooth three-folds

  • Csilla Tamás
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 6 / November 2004
    Published online by Cambridge University Press:
    15 October 2004, pp. 1561-1578
    Print publication:
    November 2004
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  • We discuss the problem of classifying crepant analytically extremal contractions $X \to Y$ from a smooth 3-fold, contracting an irreducible normal divisor D in X to a point P in Y. We prove that, if D has degree $(-K_D)^2 \geq 5$, the analytic structure of the contraction is completely determined by the isomorphism class of the exceptional locus and its normal bundle. This was previously known only for a smooth exceptional locus D.