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 inevitably specific) issues on $X$. extra accurately, it's the moduli area for $0$-dimensional subschemes of $X$ of size $n$. lately it was once learned that Hilbert schemes initially studied in algebraic geometry are heavily concerning a number of branches of arithmetic, akin to singularities, symplectic geometry, illustration theory-even theoretical physics. The dialogue within the publication displays this selection of Hilbert schemes. for instance, a development of the illustration of the endless dimensional Heisenberg algebra (i.e., Fock house) is gifted. This illustration has been studied commonly 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 distinctive and offers the unexplored hyperlink among geometry and illustration conception. The publication deals a pleasant survey of present advancements during this quickly starting to be topic. it truly is compatible as a textual content on the complicated graduate point.

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