Deresonating a Tate period

TL;DR

This paper presents a novel technique called 'deresonating' to compute monodromy periods in algebraic families, linking Apery periods of Grassmannians to special values of L-functions and distinguishing rationality of Mukai threefolds.

Contribution

It introduces a new method for computing monodromy periods by perturbing the Betti to de Rham comparison, and applies it to connect Apery periods with L-values in algebraic geometry.

Findings

Apery periods of Grassmannians G(2,N) are computed.

Apery numbers for D3 equations of Mukai threefolds are linked to specific L-values.

The argument of the L-function differs for rational and non-rational Mukai threefolds.

Abstract

We introduce a technique to compute monodromy periods in certain families of algebraic varieties by perturbing (`deresonating') the fiberwise Betti to de Rham comparison off the motivic setting. As an application, we find Apery periods of Grassmannians G(2,N) and identify the Apery numbers for the equations D3 of the Mukai threefolds with certain $L$--values. We show that the argument of the $L$--function is 3 for the rational and 2 for the non--rational Mukai threefolds.