Abstract We construct a Leray model for discrete polymatroid with arbitrary building set and we prove generalized Goresky–MacPherson formula. The first row of the is Chow ring polymatroid; Poincaré duality, Hard Lefschetz, Hodge–Riemann theorems ring. Furthermore, provide relative Lefschetz decomposition respect to deletion an element.

This course will present the basics of Hodge theory aiming to familiarize students with an important technique in complex and algebraic geometry. We start by reviewing complex manifolds, Kahler manifolds and the de Rham theorems. We then introduce Laplacians and establish the connection between harmonic forms and cohomology. The main theorems are then detailed: the Hodge decomposition and the L...