# A theory of generalized Donaldson-Thomas invariants

- Responsibility
- Dominic Joyce, Yinan Song.
- Language
- English.
- Imprint
- Providence, R.I. : American Mathematical Society, c2011.
- Physical description
- v, 199 p. ; 26 cm.
- Series
- Memoirs of the American Mathematical Society ; no.1020.

## Access

### Available online

### Math & Statistics Library

**Stacks**

Call number | Status |
---|---|

QA3 .A57 NO.1020 | Unknown |

### More options

## Creators/Contributors

- Author/Creator
- Joyce, Dominic D.
- Contributor
- Song, Yinan, 1977-

## Contents/Summary

- Bibliography
- Includes bibliographical references (p. 187-191) and index.
- Publisher's Summary
- This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which 'count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

(source: Nielsen Book Data)

## Subjects

## Bibliographic information

- Publication date
- 2011
- Series
- Memoirs of the American Mathematical Society, 0065-9266 ; no. 1020
- Note
- "May 2012, volume 217, number 1020 (second of 4 numbers)."
- ISBN
- 9780821852798 (alk. paper)
- 0821852795 (alk. paper)