Algebraic Geometry

Download E-books Lectures on Hilbert Schemes of Points on Surfaces (University Lecture Series) PDF

By Hiraku Nakajima

The Hilbert scheme $X^{[n]}$ of a floor $X$ describes collections of $n$ (not unavoidably specific) issues on $X$. extra accurately, it's the moduli area for $0$-dimensional subschemes of $X$ of size $n$. lately it was once discovered that Hilbert schemes initially studied in algebraic geometry are heavily on the topic of numerous branches of arithmetic, equivalent to singularities, symplectic geometry, illustration theory-even theoretical physics. The dialogue within the ebook displays this selection of Hilbert schemes. for instance, a development of the illustration of the limitless dimensional Heisenberg algebra (i.e., Fock house) is gifted. This illustration has been studied largely within the literature in reference to affine Lie algebras, conformal box concept, and so forth. in spite of the fact that, the development provided during this quantity is totally exact and gives the unexplored hyperlink among geometry and illustration concept. The ebook deals a pleasant survey of present advancements during this quickly growing to be topic. it truly is compatible as a textual content on the complex graduate point.

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