Fixed point scheme of the Hilbert Scheme under a 1-dimensional additive algebraic group action


Thesis Type: Doctorate

Institution Of The Thesis: Middle East Technical University, Turkey

Approval Date: 2011

Thesis Language: English

Student: Engin Özkan

Co-Supervisor: ALİ ULAŞ ÖZGÜR KİŞİSEL, ERSAN AKYILDIZ

Abstract:

In general we know that the fixed point locus of a 1-dimensional additive linear algebraic group,G_{a}, action over a complete nonsingular variety is connected. In thesis, we explicitly identify a subset of the G_{a}-fixed locus of the punctual Hilbert scheme of the d points,Hilb^{d}(P^{2}; 0),in P^{2}. In particular we give an other proof of the fact that Hilb^{d}(P^{2}; 0) is connected.