{"product_id":"a-theory-of-generalized-donaldson-thomas-invariants","title":"A Theory of Generalized Donaldson-Thomas Invariants","description":"\u003cp\u003eThis 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 $Q$.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eAuthor:\u003c\/b\u003e Dominic D. Joyce, Yinan Song\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublisher:\u003c\/b\u003e American Mathematical Soc.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublished:\u003c\/b\u003e 2011\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePages:\u003c\/b\u003e 212\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Soc.","offers":[{"title":"Default Title","offer_id":62808573477235,"sku":"9780821852798","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0812\/8115\/files\/content_cd3ef41b-3deb-4c3f-841a-565dad7f12f6.jpg?v=1777960264","url":"https:\/\/readaura.store\/products\/a-theory-of-generalized-donaldson-thomas-invariants","provider":"Read Aura","version":"1.0","type":"link"}