Explicit birational geometry of threefolds of general type
By Jungkai A. Chen, Meng Chen. 2007
71 citations recorded by the source corpus.
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 $m\geq 77$. As an application of our method, we prove Fletcher's 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 $\chi({\mathcal O}_V)\leq 1$.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/edbe14539d5c118174fb753ab8c7b8f4455814ee
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In Geometry and Topology
Citations in the corpus
- On pluricanonical systems of algebraic varieties of general type (2008, background): “t h0(V,m0KV ) ≥ 2; (b) To find an explicit function g(m0,n) (in terms of m0, n) such that the m-canonical map ϕm is birational for all m ≥ g(m0,n). This strategy works well in 3-dimensional case (e.g. [6]). For step (a), since the classification to 4-dimensional terminal singularities is still incompl”
- Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014, background): “• when κ(W) = 2 [24] (see also [22]), • when dim W = 3 [7, 8, 14, 21, 24] (see also [6]), • when X is non-uniruled, V → X has maximal variation and its general fibres have good minimal models [19] (see also [5]), • when V → X has zero variation and its general fibres have good minimal models [13].”