A Theory of Generalized Donaldson Thomas Invariants is popular PDF and ePub book, written by Dominic D. Joyce in 2012, it is a fantastic choice for those who relish reading online the Calabi-Yau manifolds genre. Let's immerse ourselves in this engaging Calabi-Yau manifolds book by exploring the summary and details provided below. Remember, A Theory of Generalized Donaldson Thomas Invariants can be Read Online from any device for your convenience.
A Theory of Generalized Donaldson Thomas Invariants Book PDF 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 $Q$.
Detail Book of A Theory of Generalized Donaldson Thomas Invariants PDF
- Author : Dominic D. Joyce
- Release : 28 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821852798
- Genre : Calabi-Yau manifolds
- Total Page : 199 pages
- Language : English
- PDF File Size : 14,5 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book A Theory of Generalized Donaldson Thomas Invariants by Dominic D. Joyce, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.
