A Theory of Generalized Donaldson-Thomas Invariants
Seiten
2012
American Mathematical Society (Verlag)
978-0-8218-5279-8 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-5279-8 (ISBN)
- Titel ist leider vergriffen;
keine Neuauflage - Artikel merken
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 $Q$.
Reihe/Serie | Memoirs of the American Mathematical Society |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 0-8218-5279-5 / 0821852795 |
ISBN-13 | 978-0-8218-5279-8 / 9780821852798 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
49,95 €
Buch | Hardcover (2022)
Freies Geistesleben (Verlag)
24,00 €