An effective upper bound for Fano indices of canonical Fano threefolds, I

Key Points

• The maximum q-fano index identified is 61, providing a new upper bound for weak fano threefolds.
• This analysis is valid for threefolds with at worst isolated canonical singularities, enhancing our understanding of Fano varieties.
• The approach utilized focuses on the geometric properties of weak fano threefolds, linking singularities to index limits.
• These findings suggest important implications in the study of algebraic geometry and singularity theory.