Subdividing simplicial virtual resolutions with homology

Abstract: While sporadic examples of virtual resolutions with homology have been constructed, their occurrence is not well understood or controlled. Our results build a new set of tools for studying virtual resolutions of monomial ideals as arising from simplicial complexes, including characterizing them by the acyclicity of certain induced subcomplexes. Using this characterization, we give a description of minimal simplicial complexes supporting virtual resolutions as well as a technique for removing homology from simplicial virtual resolutions.