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Fano Symmetric Varieties with Low Rank
Publications of the Research Institute for Mathematical Sciences
The symmetric projective varieties of rank one are all smooth and Fano by a classical result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 that are Fano. When G is semisimple we also classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 that are only quasi-Fano. Moreover, we classify the Fano symmetric G-varieties of rank 3 obtainable from a wonderful variety by a sequence of blow-upsdoi:10.2977/prims/69 fatcat:kqt7gtpqkzhuxf67mo2prmbhii