Pluricanonical systems of projective varieties of general type II

By H. Tsuji. 2004

86 citations recorded by the source corpus.

We prove that there exists a positive integer n depending only on n such that for every smooth projective n-fold of general type X defined over complex numbers, m K X gives a birational rational map from X into a projective space for every m n. This theorem gives an affirmative answer to Severi’s conjec ture.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cba514756a2abb21c15888ce2f5d0b5c09256a50

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Bergman kernels and the pseudoeffectivity of relative canonical bundles (2007, methodology): “The corollary above can be used to provide a rather simple proof of the next statement due to S. Takayama ([30], see also [16] and [ 32 ]), which is crucial in the investigation of the properties of the pluricanonical series.”
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014, background): “) depends only on d. EFFECTIVITY OF IITAKA FIBRATIONS 3 Here is a brief history of partial cases of Theorem 1.2: • when dimW= 2 [12], • when κ(W) = 1 [7], • when Wis of general type [8][21] (see also [23]), • when κ(W) = 2 [24] (see also [22]), • when dimW= 3 [14][7][24][8][21] (see also [6]), • whe”
On the birational automorphisms of varieties of general type (2010, methodology): “The first step uses some ideas of Tsuji that are used to prove some fixed multiple of KX defines a birational map for a variety X of general type; see [28], [15] and [27].”
Boundedness of pluricanonical maps of varieties of general type (2005, background): “ of KX is bounded, has attracted considerable attention, The ﬁrst author was partially supported by NSA research grant no: MDA904- 03-1-0101and by a grant from the Sloan Foundation. We are in debt to [22] and the beautiful ideas and techniques introduced in that paper. We would like to thank Meng Ch”
On pluricanonical systems of algebraic varieties of general type (2008, background): “The existence of rn for varieties of general type was proved by Hacon-Mkernan [10], Takayama [19] and Tsuji [20] and, recently, r3 ≤ 73 was proved by Chen-Chen [6, Theorem 1.”
Pluricanonical systems on algebraic varieties of general type (2006, methodology): “However the details of the proof in [ T99 ] (as well as [T01, §5], [T04b, §2.6]) are rather unclear.”