Generalized Donaldson–Thomas Invariants
Generalized Donaldson–Thomas Invariants
复制标题
广义唐纳森-托马斯不变量
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Yukinobu Toda
中科院分区：
文献类型：
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作者：
Yukinobu Toda
这是一篇与宋一男合著的更长的论文[16]的总结。Calabi-Yau 3-fold X上具有Chern特征标α的Donaldson-Thomas不变量DT α（τ）∈ Z 'count' τ -（半）稳定相干层它们在X的变形下保持不变。传统的定义只适用于没有严格τ -半稳定层的类α。Behrend证明了DT α（τ）可以表示为稳定模格式Mα st（τ）的加权欧拉特征线χ ` M α st（τ），νMst（τ）<$<$，通过一个可构造函数νMst（τ），我们称之为“Behrend函数”.讨论了广义Donaldson-Thomas不变量D <$T α（τ）∈ Q.这些都是为所有类α定义的，当它被定义时，它们等于DT α（τ）。它们在X的变形下保持不变，在稳定条件τ变化时，按已知的过壁公式进行变换。我们猜想当稳定性条件τ是“一般的”时，它们可以用积分BPS不变量D <$T α（τ）∈ Z表示.我们将理论扩展到交换范畴mod-CQ/I的表示的一个req与关系I来自一个超势W在Q上，并连接我们的想法与Szendravani的非交换唐纳森-托马斯不变量，和工作的Reineke和其他不变量计数req表示。该论文[16]与Kontsevich和Soibelman [18]最近的独立论文有显著重叠。
This is a summary of the much longer paper [16] with Yinan Song. Donaldson–Thomas invariants DT α(τ ) ∈ Z ‘count’ τ -(semi)stable coherent sheaves with Chern character α on a Calabi–Yau 3-fold X. They are unchanged under deformations of X. The conventional definition works only for classes α with no strictly τ -semistable sheaves. Behrend showed that DT α(τ ) can be written as a weighted Euler characteristic χ ` M α st(τ ), νMst(τ) ́ of the stable moduli scheme Mαst(τ ) by a constructible function νMst(τ) we call the ‘Behrend function’. We discuss generalized Donaldson–Thomas invariants D̄T α(τ ) ∈ Q. These are defined for all classes α, and are equal to DT α(τ ) when it is defined. They are unchanged under deformations of X, and transform according to a known wall-crossing formula under change of stability condition τ . We conjecture that they can be written in terms of integral BPS invariants D̂T α(τ ) ∈ Z when the stability condition τ is ‘generic’. We extend the theory to abelian categories mod-CQ/I of representations of a quiver Q with relations I coming from a superpotential W on Q, and connect our ideas with Szendrői’s noncommutative Donaldson– Thomas invariants, and work by Reineke and others on invariants counting quiver representations. The paper [16] has significant overlap with a recent, independent paper of Kontsevich and Soibelman [18].
影响因子：
3.1
作者：
Pandharipande, R.;Thomas, R. P.
通讯作者：
Thomas, R. P.