The moduli stack of stable relative ideal sheaves
Baosen Wu
TL;DR
This paper defines a moduli stack for stable relative ideal sheaves, proving it is a separated and proper Deligne-Mumford stack, advancing the foundation for relative Donaldson-Thomas theory and degeneration formulas.
Contribution
It introduces the first rigorous definition of the moduli stack of stable relative ideal sheaves and establishes its fundamental properties.
Findings
The moduli stack is separated and proper.
It forms a Deligne-Mumford stack.
Lays groundwork for relative Donaldson-Thomas invariants.
Abstract
In this paper, we propose a definition of the moduli stack of stable relative ideal sheaves, and prove that it is a separated and proper Deligne-Mumford stack. It is the first part of the project of relative Donaldson-Thomas theory of ideal sheaves on projective threefolds, which in the end provides a degeneration formula of Donaldson-Thomas invariants of threefolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models