Moduli Spaces of Stable Pairs in Donaldson-Thomas Theory

Abstract

Let $(X,{\mathcal{O}}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct a coarse moduli space for $\delta$-semistable pairs $(\mathcal{E},\varphi )$ consisting of a coherent sheaf $\mathcal{E}$ and a homomorphism $\varphi :\mathcal{D}\to \mathcal{E}$. We prove a chamber structure result and establish a connection to the moduli space of coherent systems constructed by Le Potier in \cite{LeP} and \cite{LeP2}.

arXiv commentFinal Version Published in Manuscripta Mathematica

Cited by in corpus (2)

• Moduli spaces of stable pairs
• Rank-one sheaves and stable pairs on surfaces