An effective upper bound for anti-canonical volumes of canonical $\mathbb{Q}$-Fano threefolds

Abstract

We show that the anti-canonical volume of a canonical weak $\mathbb{Q}$-Fano $3$-fold is at most $324$.

16 pages, comments are welcome; final version, to appear in IMRN

References in corpus (1)

• Shokurov's conjecture on conic bundles with canonical singularities

Cited by in corpus (3)

• Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
• On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, III
• An effective upper bound for anti-canonical volumes of singular Fano threefolds