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A Theory of Generalized Donaldson-Thomas Invariants by Dominic Joyce, Yinan Song (Paperback, 2012)

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Product Information

This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha( au)$. They are rational numbers which `count' both $ au$-stable and $ au$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $ au$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha( au)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha( au)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $ au$. 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 $f:U o{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $ u_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha( au)$ 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 $Q$.

Product Identifiers

Publisher
American Mathematical Society
ISBN-13
9780821852798
eBay Product ID (ePID)
114463220

Product Key Features

Publication Year
2012
Subject
Mathematics
Number of Pages
199 Pages
Language
English
Publication Name
A Theory of Generalized Donaldson-Thomas Invariants
Type
Textbook
Author
Dominic Joyce, Yinan Song
Format
Paperback

Additional Product Features

Country/Region of Manufacture
United States
Title_Author
Yinan Song, Dominic Joyce
Series Title
Memoirs of the American Mathematical Society

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