Zero-dimensional Donaldson–Thomas invariants of Calabi–Yau 4-folds
Zero-dimensional Donaldson–Thomas invariants of Calabi–Yau 4-folds
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DOI：
10.1016/j.aim.2018.09.011
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发表时间：
2017-12
影响因子：
1.7
通讯作者：
Yalong Cao;M. Kool
中科院分区：
文献类型：
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作者：
Yalong Cao;M. Kool
本文研究光滑射影Calabi-Yau 4-fold X上点的Hilbert格式。我们通过对重言式向量丛L [n]的Euler类与虚类积分来定义DT 4不变量。我们猜想一个公式，他们的生成系列，我们证明了在某些情况下，当L对应于一个光滑因子的X。提出了复曲面Calabi-Yau 4-折叠的一个平行等变猜想。这个猜想是证明光滑复曲面因子和验证更一般的复曲面因子在许多例子中。结合顶点计算的等变猜想，我们发现明确的正有理权重，它可以分配给固体分区。立体划分的加权生成函数由exp（M（q）− 1）给出，其中M（q）表示麦克马洪函数。
We study Hilbert schemes of points on a smooth projective Calabi–Yau 4-fold X. We define DT 4 invariants by integrating the Euler class of a tautological vector bundle L [n] against the virtual class. We conjecture a formula for their generating series, which we prove in certain cases when L corresponds to a smooth divisor on X. A parallel equivariant conjecture for toric Calabi–Yau 4-folds is proposed. This conjecture is proved for smooth toric divisors and verified for more general toric divisors in many examples. Combining the equivariant conjecture with a vertex calculation, we find explicit positive rational weights, which can be assigned to solid partitions. The weighted generating function of solid partitions is given by exp(M (q)− 1), where M (q) denotes the MacMahon function.