TL;DR
This paper proves the Relative Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial intersection cohomology on fans, advancing the understanding of geometric structures in combinatorics.
Contribution
It establishes the Relative Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial intersection cohomology sheaves on fans, a novel extension in the field.
Findings
Proved the Relative Hard Lefschetz theorem for fans.
Established the Relative Hodge-Riemann bilinear relations.
Extended geometric principles to combinatorial structures.
Abstract
We prove the Relative Hard Lefschetz theorem and the Relative Hodge-Riemann bilinear relations for combinatorial intersection cohomology sheaves on fans.
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