Pluri-canonical Systems for Surfaces of General Type
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چکیده
Let S be a compact complex surface of general type, Smin its minimal model gotten by contracting the finite number of (−1)-curves. It is a smooth surface with nef canonical line bundle KSmin . It then can be shown that Smin has at most b2 curves on which the canonical line bundleKSmin restricts to a non-ample bundle (i.e. whose intersection number with KSmin is non positive). These are (−2) smooth rational curves. Artin has shown that there is a normal surface S∗ with a finite number of rational double points gotten by contracting those curves. We will sketch two proofs of the following part of the results of Kodaira, Bombieri and Reider.
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