Now back in print, this highly regarded book has been updated to reflect recent advances in
the theory of semistable coherent sheaves and their moduli spaces, which include moduli …

Abstract Donaldson–Thomas invariants $ DT^\alpha (\tau) $ are integers which 'count'$\tau
$-stable coherent sheaves with Chern character $\alpha $ on a Calabi–Yau 3-fold $ X …

By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of
the moduli spaces Mst of stable holomorphic—resp. MHE of irreducible Hermitian-Einstein …

We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on
Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and …

Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers
DT^ a (t) which count stable sheaves with Chern character a on X, with respect to a Gieseker …

In this monograph, we define and investigate an algebro-geometric analogue of Donaldson
invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized …

A principal pair consists of a holomorphic principal G‐bundle together with a holomorphic
section of an associated Kaehler fibration. Such objects support natural gauge theoretic …

The moduli space M‾ 0, n of n pointed stable curves of genus 0 admits an action of the
symmetric group S n by permuting the marked points. We provide a closed formula for the …

Let X be a curve of genus g. A coherent system on X consists of a pair (E, V), where E is an
algebraic vector bundle over X of rank n and degree d and V is a subspace of dimension k of …

We prove that, given integers m ≥ 3 m≥ 3, r ≥ 1 r≥ 1 and n ≥ 0 n≥ 0, the moduli space of
torsion free sheaves on P^ m P m with Chern character (r, 0, ..., 0,-n)(r, 0,…, 0,-n) that are …