Exponential Hilbert series of equivariant embeddings

Wayne A. Johnson

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arXiv · 1804.04943

Exponential Hilbert series of equivariant embeddings

Wayne A. Johnson

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Abstract

In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities involving Stirling numbers of the first and second kinds.

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BibTeX RIS

Wayne A. Johnson. 2018-04-13. Exponential Hilbert series of equivariant embeddings. https://arxiv.org/abs/1804.04943

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