JournalsprimsVol. 48, No. 2pp. 235–278

Fano Symmetric Varieties with Low Rank

  • Alessandro Ruzzi

    Università di Roma La Sapienza, Italy
Fano Symmetric Varieties with Low Rank cover
Download PDF

Abstract

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 GG-varieties of rank 2 that are Fano. When GG is semisimple we also classify the locally factorial (respectively smooth) projective symmetric GG-varieties of rank 2 that are only quasi-Fano. Moreover, we classify the Fano symmetric GG-varieties of rank 3 obtainable from a wonderful variety by a sequence of blow-ups along GG-stable varieties. Finally, we classify the Fano symmetric varieties of arbitrary rank that are obtainable from a wonderful variety by a sequence of blow-ups along closed orbits.

Cite this article

Alessandro Ruzzi, Fano Symmetric Varieties with Low Rank. Publ. Res. Inst. Math. Sci. 48 (2012), no. 2, pp. 235–278

DOI 10.2977/PRIMS/69