Holomorphic polyvector fields on toric varieties via Klyachko filtrations

RESUMO

Motivated by the extended deformation theory of complex manifolds, we give a combinatorial description of holomorphic polyvector fields on a smooth compact toric variety via Klyachko's filtrations. This yields dimension and formal equivariant-character formulas and recovers the descriptions of Demazure roots and anticanonical sections.