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math.AG2026
Hodge theory for combinatorial projective bundles
Matt Larson, Ethan Partida
We prove the Hard Lefschetz theorem and Hodge-Riemann relations for certain rings which resemble the cohomology rings of projectivizations of globally generated vector bundles over…
math.AG2025
Vanishing theorems for combinatorial geometries
Christopher Eur, Alex Fink, Matt Larson
We establish strong vanishing theorems for line bundles on wonderful varieties of hyperplane arrangements, and we show that the resulting positivity properties of Euler characteris…