A Theory of Generalized Donaldson-Thomas Invariants

Dominic Joyce, Yinan Song (Autoren)

Buch | Softcover

199 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-5279-8 (ISBN)

Infos

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 $Q$.

Produkt-Details

• 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