A theory of generalized DonaldsonThomas invariants
 Author/Creator
 Joyce, Dominic D.
 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

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QA3 .A57 NO.1020

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QA3 .A57 NO.1020
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Contributors
 Contributor
 Song, Yinan, 1977
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 187191) and index.
 Publisher's Summary
 This book studies generalized DonaldsonThomas 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 wallcrossing 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
 Responsibility
 Dominic Joyce, Yinan Song.
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1020
 Note
 "May 2012, volume 217, number 1020 (second of 4 numbers)."
 ISBN
 9780821852798 (alk. paper)
 0821852795 (alk. paper)