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O. V. Chuvashova Moscow State University Moscow, Russia chuvasho@mccme.ru

Invariant Hilb ert schemes
Let X be an affine toric variety under an algebraic torus T and let T T be a subtorus. The general T -orbit closures and their limits are parameterized by the main component H0 of the toric Hilbert scheme (whose existence follows from work of M. Haiman and T. Sturmfels [3]). Further, the quotient T/T acts on H0 with an open orbit. We describe the fan of this toric variety [2]. We shall also give some examples of construction of the invariant Hilbert scheme [1], which is a generalization of a toric Hilbert scheme on the case of a reductive group action. References [1] V. Alexeev and Algebraic Geom. [2] O. Chuvashova, [3] M. Haiman and (2004), 725­769. M. Brion, Moduli of affine schemes with reductive group action, J. 14 (2005), no. 1, 83-117. The main component of the Hilbert scheme, arxiv: math.AG/0603703 B. Sturmfels, Multigraded Hilbert schemes, J. Algebraic Geom. 13

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