Computation of Grothendieck motives of moduli spaces and the Mozgovoy Conjecture

Abstract

Presentamos motives, un nuevo paquete de Python integrado en el entorno SymPy, dise˜nado para simplificar y manipular ecuaciones en λ-anillos. El objetivo del paquete es facilitar el estudio de expresiones mot´ıvicas, y para ello incluye muchos motivos preprogramados, as´ı como la implementaci´on y optimizaci´on de un algoritmo que convierte cualquier expresi´on en un polinomio en sus operaciones λ o Adams. El paquete ha sido utilizado para estudiar la f´ormula conjetural de Mozgovoy para el motivo del espacio de moduli de L-twisted Higgs bundles, compar´andola con una expresi´on probada que representa el mismo motivo.

We present motives, a new Python package integrated into the SymPy environment designed to simplify and manipulate equations in λ-rings. The package’s aim is to facilitate the study of motivic expressions, and to this end it includes many pre-programmed motives, as well as implementing and optimizing an algorithm that turns any expression into a polynomial of its λ or its Adams operations. The package was used to study Mozgovoy’s conjectural formula for the motive of the moduli space of L-twisted Higgs bundles by comparing it to a proven expression that represents the same motive.