A Theory of Generalized Donaldson-Thomas Invariants PDF
by Dominic Joyce
Description
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 $Q$.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:199 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9780821887523
Information
-
Download - Immediately Available
- Format:PDF
- Pages:199 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9780821887523
