The projective coinvariant algebra, Young invariants and bigraded coordinate rings of Segre embeddings
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911451040448512 |
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| author | Szendrői, Balázs |
| author_facet | Szendrői, Balázs |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The projective coinvariant algebra, Young invariants and bigraded coordinate rings of Segre embeddings Szendrői, Balázs Algebraic Geometry Commutative Algebra Combinatorics 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. |
| title | The projective coinvariant algebra, Young invariants and bigraded coordinate rings of Segre embeddings |
| topic | Algebraic Geometry Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2602.15017 |