Gorenstein Fano Threefolds with Base Points in the Anticanonical System Priska Jahnke and Ivo Radloff
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چکیده
In the classification of Fano varieties, those which are not “Gino Fano”, i.e., where −KX is ample but not very ample, are usually annoying. In the beginning of his classification of Fano threefolds, Iskovskikh listed those for which |−KX | is not free. The purpose of this article is to see how his result extends to the canonical Gorenstein case. If X is a Gorenstein Fano threefold with at worst canonical singularities, and Bs |−KX | 6 = ∅, then the rational map defined by |−KX | goes to a surface W , which is a rational ruled surface Σe with e ≥ 0 or Ĉd, the cone over a rational normal curve of degree d. The following Theorem lists the possible pairs (X,W ):
منابع مشابه
Threefolds with Big and Nef Anticanonical Bundles Ii Priska Jahnke, Thomas Peternell, and Ivo Radloff
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