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

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

Written by:GAPA
主题
Zero dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
活动时间
-
活动地址
Room 415 (New Math. Building), Sun Yat-sen University
主讲人
Yalong Cao (Oxford University)

Abstract:  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.