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This is a Quantitative Study study.

September 29, 2025Open Access

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

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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.

Research reveals that the q-fano index is limited to 61 in weak fano threefolds with canonical singularities.

Let X be a Q-factorial weak Fano $3$-fold with at worst isolated canonical singularities. We show that the Q-Fano index of X is at most $61$.

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Jiang et al. (2025) studied this question.

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Research reveals that the q-fano index is limited to 61 in weak fano threefolds with canonical singularities.

Let X be a Q-factorial weak Fano $3$-fold with at worst isolated canonical singularities. We show that the Q-Fano index of X is at most $61$.