Classification of arithmetically Gorenstein divisors on some Fano varieties (Q842511)

Let \(Y\) be a smooth, connected, subcanonical and linearly normal Fano variety of dimension \(n\) and index \(r\) in some projective space. Assume that \(3 \leq n \leq 2r-1\), and that the rank \(\rho (Y)\) of the Picard group is at least 2. The authors give a complete classification of the arithmetically Gorenstein divisors \(G\) on \(Y\). They show that ``usually'' \(G\) is cut out by a hypersurface, but there are three exceptions, which they describe in detail. The proof is a case-by-case analysis, starting with the classification of such Fano varieties by Wiśniewski. This analysis reduces the problem to a short list of possibilities, which are then carefully analyzed.