Adjoint pluricanonical systems on varieties of general type

作者：Di Biagio Lorenzo^*

来源：Advances in Geometry, 2013, 13(3): 471-484.

DOI：10.1515/advgeom-2012-0033

• Pluricanonical systems
• adjoint linear systems
• varieties of general type

We study non-vanishing and birationality of big pluricanonical adjoint linear systems on a variety of general type X. In particular given L big and with sufficiently large volume, if X is a surface we prove that h(0) (2K(X) + L) 6 not equal 0 and that vertical bar 3K(X) + 2L vertical bar gives a birational map; if X is a threefold we prove that h(0) (6K(X) + 5L) 6 not equal 0 and that vertical bar 8K(X) + 7L vertical bar gives a birational map. We find analogous explicit results also for fourfolds of general type.

• 出版日期2013-7