An explicit construction of derived moduli stacks of Harder-Narasimhan filtrations

TL;DR

This paper provides an explicit construction of derived moduli stacks for Harder-Narasimhan filtrations on projective schemes, enhancing understanding of their deformation theory and comparing with existing methods.

Contribution

It introduces a new explicit construction of derived moduli stacks of Harder-Narasimhan filtrations using established methods and compares it with prior approaches.

Findings

Explicit construction of derived moduli stacks

Description of derived deformation theory of filtered sheaves

Comparison with Di Natale's construction

Abstract

In this article, we give an explicit construction of the derived moduli stack of Harder-Narasimhan filtrations on a connected projective scheme over an algebraically closed field k of characteristic 0 by using methods by Behrend, Ciocan-Fontanine, Hwang and Rose. Moreover, we describe the derived deformation theory of a filtered sheave on a connected projective scheme over k and compare our construction with a construction by Di Natale.