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Characterising certain compactifications of frames with special attention to Freudenthal

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0 Published in 2021 at "Algebra universalis"

DOI: 10.1007/s00012-021-00708-7

Abstract: We introduce the definition of h - perfect elements relative to a compactification $$h:M\longrightarrow L$$ h : M ⟶ L and show that if a collection of all such elements is a basis, then the… read more here.

Keywords: compactification; certain compactifications; characterising certain; full compact ... See more keywords

The intersection cohomology of the Satake compactification of $${\mathcal {A}}_g$$Ag for $$g \le 4$$g≤4

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1 Published in 2017 at "Mathematische Annalen"

DOI: 10.1007/s00208-016-1491-1

Abstract: We completely determine the intersection cohomology of the Satake compactifications $${{\mathcal {A}}_{2}^{\mathrm{Sat}}},{{\mathcal {A}}_{3}^{\mathrm{Sat}}}$$A2Sat,A3Sat, and $${{\mathcal {A}}_{4}^{\mathrm{Sat}}}$$A4Sat, except for $${ IH}^{10}({{\mathcal {A}}_{4}^{\mathrm{Sat}}})$$IH10(A4Sat). We also determine all the ingredients appearing in the decomposition theorem applied to the… read more here.

Keywords: compactification; mathcal mathrm; mathrm sat; cohomology ... See more keywords

Newton Polyhedra and Good Compactification Theorem

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0 Published in 2020 at "Arnold Mathematical Journal"

DOI: 10.1007/s40598-020-00157-5

Abstract: A new transparent proof of the well-known good compactification theorem for the complex torus $$({\mathbb {C}}^*)^n$$ ( C ∗ ) n is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in… read more here.

Keywords: compactification; compactification theorem; good compactification; newton polyhedra ... See more keywords

Electroid varieties and a compactification of the space of electrical networks

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0 Published in 2018 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2018.09.014

Abstract: We construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally nonnegative Grassmannian, and… read more here.

Keywords: compactification; compactification space; electroid varieties; electrical networks ... See more keywords

Satake compactification of analytic Drinfeld modular varieties

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0 Published in 2021 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2020.09.018

Abstract: Abstract We construct a normal projective rigid analytic compactification of an arbitrary Drinfeld modular variety whose boundary is stratified by modular varieties of smaller dimensions. This generalizes work of Kapranov. Using an algebraic modular compactification… read more here.

Keywords: drinfeld modular; compactification; analytic drinfeld; analytic compactification ... See more keywords

PARABOLIC COMPACTIFICATION OF HOMOGENEOUS SPACES

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0 Published in 2019 at "Journal of the Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748019000513

Abstract: Abstract In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$ . The key to this approach is that in each case $G/P$ is the… read more here.

Keywords: parabolic compactification; geometry; compactification; compactification homogeneous ... See more keywords

Theory of flavors: String compactification

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0 Published in 2018 at "Physical Review D"

DOI: 10.1103/physrevd.98.055005

Abstract: We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through Z12-I orbifold compactification. It is… read more here.

Keywords: compactification; string compactification; theory flavors; flavors string ... See more keywords

Arzelà-Ascoli theorem via the Wallman compactification

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0 Published in 2017 at "Quaestiones Mathematicae"

DOI: 10.2989/16073606.2017.1381653

Abstract: Abstract In the paper, we recall the Wallman compactification of a Tychonoff space T (denoted by Wall(T)) and the contribution made by Gillman and Jerison. Motivated by the Gelfand-Naimark theorem, we investigate the homeomorphism between… read more here.

Keywords: compactification; arzel ascoli; ascoli theorem; wallman compactification ... See more keywords