Explicit birational geometry of 3-folds and 4-folds of general type, III
نویسندگان
چکیده
منابع مشابه
On the birational geometry of toric Fano 4-folds
In this Note, we announce a factorization result for equivariant birational morphisms between toric 4-folds whose source is Fano: such a morphism is always a composite of blow-ups along smooth invariant centers. Moreover, we show with a counterexample that, differently from the 3-dimensional case, even if both source and target are Fano, the intermediate varieties can not be chosen Fano. Sur la...
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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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If X is a smooth complex projective 3-fold with ample canonical divisor K, then the inequality K ≥ 2 3 (2pg − 7) holds, where pg denotes the geometric genus. This inequality is nearly sharp. We also give similar, but more complicated, inequalities for general minimal 3-folds of general type. Introduction Given a minimal surface S of general type, we have two famous inequalities, which play cruc...
متن کاملExplicit Birational Geometry of Threefolds of General Type, Ii
Let V be a complex nonsingular projective 3-fold of general type. We shall give a detailed classification up to baskets of singularities on a minimal model of V . We show that the mcanonical map of V is birational for all m ≥ 73 and that the canonical volume Vol(V ) ≥ 1 2660 . When χ(OV ) ≤ 1, our result is Vol(V ) ≥ 1 420 , which is optimal. Other effective results are also included in the paper.
متن کاملExplicit Birational Geometry of Threefolds of General Type, I
Let V be a complex nonsingular projective 3-fold of general type. We prove P12(V ) := dimH (V, 12KV ) > 0 and Pm0(V ) > 1 for some positive integer m0 ≤ 24. A direct consequence is the birationality of the pluricanonical map φm for all m ≥ 126. Besides, the canonical volume Vol(V ) has a universal lower bound ν(3) ≥ 1 63·126 .
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2014
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x14007817