Projective 3-folds of General Type with Χ = 1
نویسنده
چکیده
There are many examples of 3-folds of general type with χ(O) = 1 found by Fletcher and Reid about twenty years ago. Fletcher has ever proved P12(X) ≥ 1 and P24(X) ≥ 2 for all minimal 3-folds X of general type with χ(OX) = 1. In this paper, we improve on Fletcher’s method. Our main result is that φm is birational onto its image for allm ≥ 63. To prove this we will show Pm ≥ 1 for all m ≥ 14 and P2l+18 ≥ 3 for all l ≥ 0.
منابع مشابه
Explicit Birational Geometry of Threefolds of General Type
Let V be a complex nonsingular projective 3-fold of general type. We prove that P12(V ) > 0 and P24(V ) > 1. We also prove that the canonical volume has an universal lower bound Vol(V ) ≥ 1/2660 and that the pluri-canonical map φm is birational onto its image for all m ≥ 77. As an application of our method, we prove Fletcher’s conjecture on weighted hyper-surface 3-folds with terminal quotient ...
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We prove that the canonical volume K ≥ 1 30 for all 3-folds of general type with χ(O) ≤ 0. This bound is sharp.
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There are many examples of 3-folds of general type with χ(O) = 1 found by Fletcher and Reid about twenty years ago. Iano-Fletcher has ever proved P12(X) ≥ 1 and P24(X) ≥ 2 for all minimal 3-folds X of general type with χ(OX) = 1. In this paper, we improve on Fletcher’s method. Our main results are: Pm ≥ 1 for all m ≥ 14, P18 ≥ 2, P20 ≥ 3 and that φm is birational onto its image for all m ≥ 88 w...
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