On a sufficient condition for a Fano manifold to be covered by rational $N$-folds

TL;DR

This paper proves Suzuki's conjecture that certain positivity conditions on a Fano manifold's Chern character ensure it is covered by rational N-folds, using combinatorial properties of Bernoulli numbers.

Contribution

It establishes a new sufficient condition for Fano manifolds to be covered by rational N-folds based on Chern character positivity and Bernoulli number properties.

Findings

Proved Suzuki's conjecture on Fano manifolds.

Connected Chern character positivity to rational N-fold coverage.

Utilized combinatorial properties of Bernoulli numbers in proof.

Abstract

In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern character, then it can be covered by rational $N$-folds. We prove this conjecture by using purely combinatorial properties of Bernoulli numbers.