Journal of the Ramanujan Mathematical Society
Volume 38, Issue 4, December 2023 pp. 325–354.
Multifiltrations
Authors:
José Ignacio Burgos Gil and Vivek Mohan Mallick
Author institution:
ICMAT, Campus Cantoblanco, Madrid, Spain.
Summary:
This paper deals with properties of filtrations on vector spaces indexed by
partially ordered finitely generated abelian groups, which we call
multifiltrations. We discuss the usual properties of filtrations, like
exhaustivity and separatedness in the setting of multifiltrations and we
introduce a new notion, regular multifiltrations, that has no analogue for
classical filtrations. As applications, we provide a reinterpretation of
Klyachko and Perling descriptions of torus-equivariant torsion-free coherent
sheaves on a toric variety, and give a simple formula for pull-backs of such
sheaves. We also explore the occurrence of such multifiltration among finite
dimensional representations of connected, solvable groups.
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