Homological Action of the Modular Group on Some Cubic Moduli Spaces

On Atkin-Lehner correspondences on Siegel spaces

‎We introduce a higher dimensional Atkin-Lehner theory for‎ ‎Siegel-Parahoric congruence subgroups of $GSp(2g)$‎. ‎Old‎ ‎Siegel forms are induced by geometric correspondences on Siegel‎ ‎moduli spaces which commute with almost all local Hecke algebras‎. ‎We also introduce an algorithm to get equations for moduli spaces of‎ ‎Siegel-Parahoric level structures‎, ‎once we have equations for prime l...

Genus stabilization for the components of moduli spaces of curves with symmetries

In a previous paper (Groups, Geometry, and Dynamics, 2015), we introduced a new homological invariant ε for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant ε, if the genus g′ of the quotient curve satisfies g′ 0, is irreducible (and non-empty if and only...

Some result on modular hyperconvex spaces

On Some Moduli Spaces of Stable Vector Bundles on Cubic and Quartic Threefolds

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles.

Fixed Point Results for Cyclic (α,β)-Admissible Type F-Contractions‎ ‎in Modular Spaces

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...