Download E-books Lectures on Hilbert scheme of points on surfaces (draft, AMS 1999) PDF

By Nakajima H.

Within the spring of 1996, I gave a chain of lectures at the Hilbert schemes of issues on surfaces at division of Mathematical Sciences, collage of Tokyo. the aim of the lectures used to be to debate numerous houses of the Hilbert schemes of issues on surfaces. even though it used to be no longer spotted till lately, the Hilbert schemes have courting with many different department of arithmetic, reminiscent of topology, hyper-Kahler geometry, symplectic geometry, singularities, and illustration thought. this can be mirrored to this word: each one bankruptcy, which approximately corresponds to at least one lecture, discusses assorted issues. those lectures have been meant for graduate scholars who've easy wisdom on algebraic geometry and traditional topology. the one effects to be able to be used yet now not proved during this notice are Grothendieck's development of the Hilbert scheme (Theorem 1.1) and effects on intersection cohomology (§6.1). i like to recommend to the reader to just accept those effects while he/she isn't really conversant in them. i've got attempted to give the opportunity to learn each one bankruptcy independently. i feel that it's virtually winning. The interdependence of chapters is figured within the subsequent web page. The damaged arrows suggest that we want simply the assertion of ends up in the outgoing bankruptcy, and don't desire its evidence. Sections 9.1,9.3 are according to A. Matsuo's lectures. His lectures contained Monster and Macdonald polynomials. I remorse omitting those matters. i'm hoping to appreciate those through Hilbert schemes in destiny. The be aware used to be ready through T. Gocho and N. Nakamura. i want to thank them for his or her efforts. i'm additionally thankful to A. Matsuo and H. Ochiai for his or her reviews throught the lectures. specific thank you are because of G. Ellingsrud, I. Grojnowski, ok. Hasegawa, N. Hitchin, Y. Ito, A. King, G. Kuroki, G. Segal, and S. Str0mme for discussions on ends up in this observe.

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