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Explicit birational geometry of threefolds of general type

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 نشر من قبل Meng Chen
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Jungkai A. Chen




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Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V)>0$ and $P_{24}(V)>1$ (which answers an open problem of J. Kollar and S. Mori). We also prove that the canonical volume has an universal lower bound $text{Vol}(V) geq 1/2660$ and that the pluri-canonical map $Phi_m$ is birational onto its image for all $mgeq 77$. As an application of our method, we prove Fletchers conjecture on weighted hyper-surface 3-folds with terminal quotient singularities. Another featured result is the optimal lower bound $text{Vol}(V)geq {1/420}$ among all those 3-folds $V$ with $chi({mathcal O}_V)leq 1$.



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