Moduli of parabolic sheaves on a polarized logarithmic scheme

TL;DR

This paper extends the construction of moduli spaces of parabolic sheaves to polarized logarithmic schemes, allowing for variable weights, thereby broadening the applicability of such moduli spaces in algebraic geometry.

Contribution

It generalizes existing moduli space constructions to the setting of projective fine saturated log schemes with fixed global charts and introduces moduli spaces without fixed weights.

Findings

Constructed moduli spaces for parabolic sheaves on log schemes.

Extended the theory to include variable weights.

Provided a framework for future research in logarithmic geometry.

Abstract

We generalize the construction of moduli spaces of parabolic sheaves given by Maruyama and Yokogawa in [MY92] to the case of a projective fine saturated log scheme with a fixed global chart. Furthermore we construct moduli spaces of parabolic sheaves without fixing the weights.