geometry-topology / Enumerative geometry

Positivity of Chern Classes of Symmetric Powers

The total Chern class of $\mathrm{Sym}^d(\mathbb{C}^n)$ as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.

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geometry-topologyMay 24, 2026Significance 15/100Registry: unreviewed

Positivity of Chern Classes of Symmetric Powers

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The total Chern class of $\mathrm{Sym}^d(\mathbb{C}^n)$ as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.

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The total Chern class of $\mathrm{Sym}^d(\mathbb{C}^n)$ as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.

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Positivity of Chern Classes of Symmetric Powers — Mathematical Frontier Network