The classification of smooth well-formed Fano weighted complete intersections

Abstract

We show that the set of families of smooth well-formed Fano weighted complete intersections admits a natural partition with respect to the variance $\mathrm{var}(X)=\mathrm{coind}(X)-\mathrm{codim}(X)$. Moreover, we obtain the classification of smooth well-formed Fano weighted complete intersections of small variance. We also prove that the anticanonical linear system on a smooth well-formed Fano weighted complete intersection of anticanonical degree one is never base-point free.

26 pages. A small fix in Example 1.10 and Remark 1.11

References in corpus (1)

• Automorphisms of weighted complete intersections

Cited by in corpus (1)

• Belyi's theorem for smooth complete intersections of general type in generalised Grassmannians and weighted projective spaces