arXiv subjects
Publications and source records attributed to Vivek Mohan Mallick.
For an affine $T$-variety $X$ with the action of a torus $T$, this paper provides a combinatorial description of $X$ with respect to the action of a subtorus $T' \subset T$ in terms of a $T/T'$-invariant pp-divisor. We also describe the corresponding GIT fan.
The paper provides a computation of the equivariant Chow group of a rational, complete, complexity one $T$-variety
We study multihomogeneous spaces corresponding to ${\mathbb Z}^n$-graded algebras over an algebraically closed field of characteristic 0 and their relation with the description of $T$-varieties.
The paper explores the relation between Perling's toric Proj of a multigraded ring A associated with a toric variety (tProj A), and Brenner and Schroer's homogeneous spectrum ProjMH A of the same ring. We show that there is always a canonical open embedding and study a criterion for them to be isomorphic.
We develop a point-free approach for constructing the Nakano-Vashaw-Yakimov-Balmer spectrum of a noncommutative tensor triangulated category under some mild assumptions. In particular, we provide a conceptual way of classifying radical thick tensor ideals of a noncommutative tensor triangulated category using frame theoretic methods, recovering the universal support data in the process. We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology.
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, Perling et al's description 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.
This paper studies the Eilenberg Moore construction on DG categories. As applications one proves results on factoring of monads as composition of a pair of adjoint exact functors and further applications to reinterpretations of equivariant traingulated categories.