On the birational geometry of $\mathbf{Q}$-Fano threefolds of large Fano index, I

Abstract

We investigate the rationality problem for $\mathbf{Q}$-Fano threefolds of Fano index $\ge 2$.

arXiv comment24 pages, LaTeX, submitted to Edge volume 2

References in corpus (4)

• Divisorial contractions in dimension three which contract divisors to smooth points
• Which quartic double solids are rational?
• Q-Fano threefolds of index $7$
• A remark on resolution of terminal singularities

Cited by in corpus (2)

• Kawamata-Miyaoka-type inequality for $\mathbb{Q}$-Fano varieties with canonical singularities II: Terminal $\mathbb{Q}$-Fano threefolds
• On the birational geometry of sextic threefold hypersurface in $\mathbf{P}(1,1,2,2,3)$