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Tautological classes of matroids
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Tautological classes of matroids
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We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a Chow-theoretic description and a log-concavity property for a 4-variable transformation of the Tutte polynomial, and by establishing an exceptional Hirzebruch-Riemann-Roch-type formula for permutohedral varieties that translates between K-theory and Chow theory.
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Cited by 1 Pith paper
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The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
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