On the Euler characteristics of certain moduli spaces of 1-dimensional subschemes.

Date: 
Tuesday, August 15, 2017 - 1:00pm
Location: 
117 MSB
Speaker: 
Mazen Alhwaimel (Advisor: Prof. Zhenbo Qin)

Abstract: 

In the paper titled ”Gromov-Witten theory and Donaldson-Thomas theory, I”, by D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande, the authors proposed a conjecture regarding  the reduced partition function of Thomas-Donaldson invariants for certain moduli spaces. W.-P, Li and Zhenbo Qin, proposed an analogue for that conjecture for the reduced partition function of the Euler Characteristics regarding some moduli spaces parametrizing certain closed subschemes in a smooth projective variety. Li and Qin were able to investigate the conjecture under certain assumptions. In this thesis, we will continue to generalize their ideas, and further verify the proposed conjecture. We will mainly use virtual Hodge polynomials to reduce the computations of the Euler characteristics of those moduli spaces to simpler ones which will consist of the Euler characteristics of the Hilbert schemes of points, which have already been computed, and other moduli spaces parametrizing closed subschemas of a local model where we apply torus actions and combinatorial techniques to obtain their Euler characteristics.