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S. K. Geetha - One of the best experts on this subject based on the ideXlab platform.

  • F-semigroup Compactifications
    Fuzzy Sets and Systems, 1992
    Co-Authors: S. K. Geetha
    Abstract:

    Abstract In this paper we discuss Compactifications of a fuzzy topological semigroup. We prove that corresponding to the Bohr compactification of a topological semigroup, the Bohr fuzzy compactification exists for a topologically generated fuzzy topological semigroup. We also introduce F-semigroup compactification analogous to the notion of semigroup Compactifications of topological semigroups, and prove that the set of all F-semigroup Compactifications of a fuzzy topological semigroup is an upper complete semilattice.

Pekka Salmi - One of the best experts on this subject based on the ideXlab platform.

Romyar T Sharifi - One of the best experts on this subject based on the ideXlab platform.

  • Compactifications of s arithmetic quotients for the projective general linear group
    arXiv: Number Theory, 2015
    Co-Authors: Takako Fukaya, Kazuya Kato, Romyar T Sharifi
    Abstract:

    Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and non-archimedean places in S, respectively. We construct Compactifications of the quotient of X by S-arithmetic subgroups of PGL_d(F). The constructions make delicate use of reductive Borel-Serre spaces for archimedean places and polyhedral and seminorm Compactifications at nonarchimedean places. We also briefly discuss a few potential applications of our compacifications.

  • Compactifications of s arithmetic quotients for the projective general linear group
    Conference on Elliptic Curves Modular Forms and Iwasawa Theory held in honour of the 70th birthday of John H. Coates 2015, 2015
    Co-Authors: Takako Fukaya, Kazuya Kato, Romyar T Sharifi
    Abstract:

    Let F be a global field, let S be a nonempty finite set of places of F which contains the archimedean places of F, let \(d\geqslant 1\), and let \(X =\prod _{v\in S} X_v\) where \(X_v\) is the symmetric space (resp., Bruhat-Tits building) associated to \({{\mathrm{PGL}}}_d(F_v)\) if v is archimedean (resp., non-archimedean). In this paper, we construct Compactifications \(\Gamma \backslash \bar{X}\) of the quotient spaces \(\Gamma \backslash X\) for S-arithmetic subgroups \(\Gamma \) of \({{\mathrm{PGL}}}_d(F)\). The constructions make delicate use of the maximal Satake compactification of \(X_v\) (resp., the polyhedral compactification of \(X_v\) of Gerardin and Landvogt) for v archimedean (resp., non-archimedean). We also consider a variant of \(\bar{X}\) in which we use the standard Satake compactification of \(X_v\) (resp., the compactification of \(X_v\) due to Werner).

Armand Borel - One of the best experts on this subject based on the ideXlab platform.

Richard Wentworth - One of the best experts on this subject based on the ideXlab platform.

  • complex algebraic Compactifications of the moduli space of hermitian yang mills connections on a projective manifold
    arXiv: Differential Geometry, 2018
    Co-Authors: Daniel Greb, Benjamin Sibley, Matei Toma, Richard Wentworth
    Abstract:

    In this paper we study the relationship between three Compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli space of stable holomorphic vector bundles, and as such it admits an algebraic compactification by Gieseker-Maruyama semistable torsion-free sheaves. A recent construction due to the first and third authors gives another compactification as a moduli space of slope semistable sheaves. In the present article, following fundamental work of Tian generalising the analysis of Uhlenbeck and Donaldson in complex dimension two, we define a gauge theoretic compactification by adding certain ideal connections at the boundary. Extending work of Jun Li in the case of bundles on algebraic surfaces, we exhibit comparison maps from the sheaf theoretic Compactifications and prove their continuity. The continuity, together with a delicate analysis of the fibres of the map from the moduli space of slope semistable sheaves allows us to endow the gauge theoretic compactification with the structure of a complex analytic space.

  • Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
    arXiv: Algebraic Geometry, 1993
    Co-Authors: Aaron Bertram, Georgios Daskalopoulos, Richard Wentworth
    Abstract:

    Two Compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective scheme and is dominated by the algebraic compactification arising as a Grothendieck Quot scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as Gromov invariants) on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.