A theory of generalized Donaldson-Thomas invariants /
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| Author / Creator: | Joyce, Dominic D. |
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| Imprint: | Providence, R.I. : American Mathematical Society, c2012. |
| Description: | v, 199 p. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 1020 Memoirs of the American Mathematical Society ; no. 1020. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8778928 |
| 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 $Q$. |
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| Item Description: | "May 2012, volume 217, number 1020 (second of 4 numbers)." |
| Physical Description: | v, 199 p. ; 26 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9780821852798 0821852795 |
| ISSN: | 0065-9266 ; |
