Footnotes to a footnote of a paper by Fano

Abstract

Following a suggestion in a footnote of the paper [1] by Fano, we give a direct proof of the fact that one of the two Fano threefolds of degree 72 in ${\mathbb{P}}^{38}$ is isomorphic to the anticanonically embedded weighted projective space $\mathbb{P}(1,1,4,6)$.

KEYWORDS:

• Fano varieties
• weighted projective spaces

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 14E25
• 14J30
• 14J45
• 14M20

Acknowledgments

The author is a member of GNSAGA of the Istituto Nazionale di Alta Matematica “F. Severi”. The author wants to thank Yuri Prokhorov for useful e-mail exchanges of ideas on the topic of this note.