The Lefschetz standard conjectures for 4d-dimensional Kummer-type hyper-Kaehler varieties

TL;DR

This paper proves the Lefschetz standard conjectures for 4d-dimensional Kummer-type hyper-Kaehler varieties, assuming a conjecture by Buchweitz and Flenner, advancing understanding in algebraic geometry.

Contribution

It establishes the Lefschetz standard conjectures for a new class of hyper-Kaehler varieties under a specific conjectural assumption.

Findings

Proves the conjecture for 4d-dimensional Kummer-type varieties

Depends on the Buchweitz-Flenner conjecture

Advances the theory of algebraic cycles in hyper-Kaehler varieties

Abstract

Contingent upon a conjecture of Buchweitz and Flenner, we prove the Lefschetz standard conjectures for 4d-dimensional projective varieties of generalized Kummer deformation type.