GAGP系列讲座(曹亚龙 7.16)

发布人:周妍 发布日期:2018-07-13

GAGP系列讲座(曹亚龙 7.16


题目:Zero dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds

主讲人:曹亚龙 博士后 (牛津大学)

时间:2018/7/16 下午16:00-17:30




We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold X and define DT4 invariants by integrating the Euler class of a tautological vector bundle 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. This is joint work with Martijn Kool.