An effective upper bound for anti-canonical volumes of singular Fano threefolds

Abstract

For a real number $0<\epsilon <1/3$, we show that the anti-canonical volume of an $\epsilon$-klt Fano $3$-fold is at most $3200/{\epsilon }^4$ and the order $O(1/{\epsilon }^4)$ is sharp.

15 pages, comments are welcome

References in corpus (1)

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