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arXiv · 2602.15017

The projective coinvariant algebra, Young invariants and bigraded coordinate rings of Segre embeddings

Balázs Szendrői
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Abstract

This paper studies a flat degeneration P_n of the classical coinvariant algebra R_n, a bigraded Artinian Gorenstein algebra that arises from the coordinate ring of the Segre embedding of the n-fold self-product of the projective line. The Frobenius character of P_n is computed by a natural bigraded refinement of the classical Lusztig--Stanley formula for the character of the coinvariant algebra. Young invariants in P_n get related to coordinate rings of general Segre embeddings of products of projective spaces; their bigraded Hilbert polynomials get expressed in terms of major-descent generating functions of words in multisets. Relations to the diagonal coinvariant algebra, cohomological interpretations including quantum cohomology, and Garsia-Stanton-style bases are also explored.

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Balázs Szendrői. 2026-02-16. The projective coinvariant algebra, Young invariants and bigraded coordinate rings of Segre embeddings. https://arxiv.org/abs/2602.15017

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