Gundy–Varopoulos martingale transforms and their projection operators on manifolds and vector bundles
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Annalen"
DOI: 10.1007/s00208-019-01825-4
Abstract: This paper proves the $$L^p$$Lp boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms à la Gundy–Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples and… read more here.
Keywords: gundy varopoulos; varopoulos martingale; manifolds vector; vector bundles ... See more keywords
Toric vector bundles: GAGA and Hodge theory
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02605-6
Abstract: We prove a GAGA-style result for toric vector bundles with smooth base and give an algebraic construction of the Frölicher approximating vector bundle that has recently been introduced by Dan Popovici using analytic techniques. Both… read more here.
Keywords: vector bundles; vector; gaga hodge; toric vector ... See more keywords
Cohomology of vector bundles and non-pluriharmonic loci
Sign Up to like & getrecommendations! Published in 2020 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02634-1
Abstract: In this paper, we study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem. read more here.
Keywords: non pluriharmonic; vector bundles; bundles non; cohomology vector ... See more keywords
Vector Bundles on P1ℤ with Simple Jumps
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DOI: 10.1007/s10958-018-3901-2
Abstract: Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is… read more here.
Keywords: simple jumps; vector; bundles simple; vector bundles ... See more keywords
Spanned vector bundles with high rank and no trivial factor on n-folds
Sign Up to like & getrecommendations! Published in 2017 at "Afrika Matematika"
DOI: 10.1007/s13370-016-0430-3
Abstract: Let X be a smooth n-fold, $$n\ge 3$$n≥3, and $$\mathcal {L}$$L a spanned and ample line bundle on X with $$h^1(\mathcal {O}_X)=0$$h1(OX)=0. Let $$\mathcal {E}$$E be a spanned rank r vector bundle on X with… read more here.
Keywords: mathcal mathcal; trivial factor; spanned vector; vector bundles ... See more keywords
Weight decompositions of Thom spaces of vector bundles in rational homotopy
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Homotopy and Related Structures"
DOI: 10.1007/s40062-019-00243-2
Abstract: Motivated by the theory of representability classes by submanifolds, we study the rational homotopy theory of Thom spaces of vector bundles. We first give a Thom isomorphism at the level of rational homotopy, extending work… read more here.
Keywords: rational homotopy; thom spaces; homotopy; vector bundles ... See more keywords
Universal degeneracy classes for vector bundles on P1 bundles
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.107563
Abstract: Abstract Given a vector bundle on a P 1 bundle, the base is stratified by degeneracy loci measuring the splitting type of the vector bundle restricted to each fiber. The classes of these degeneracy loci… read more here.
Keywords: degeneracy; vector bundle; vector bundles; degeneracy loci ... See more keywords
On equivalence of the second order linear differential operators, acting in vector bundles
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2020.103749
Abstract: Abstract The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally associated with differential operators, are… read more here.
Keywords: differential operators; vector bundles; linear differential; acting vector ... See more keywords
Construction of symplectic vector bundles on projective space P3
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2020.103949
Abstract: Abstract The moduli spaces of symplectic vector bundles of arbitrary rank on projective space P 3 are far from being well-understood. By now the only type of such bundles having satisfactory description are the so-called… read more here.
Keywords: projective space; vector; symplectic vector; vector bundles ... See more keywords
Brauer and Picard groups of moduli spaces of parabolic vector bundles on a real curve
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DOI: 10.1080/00927872.2023.2193640
Abstract: We determine the Brauer group and Picard group of the moduli space $U^{' s}_{L,par}$ of stable parabolic vector bundles of rank $r$ with determinant $L$ on a real curve $Y$ of arithmetic genus $g \,\ge\,… read more here.
Keywords: brauer picard; real curve; parabolic vector; vector bundles ... See more keywords
Quantization of Vector Bundles on Lagrangian Subvarieties
Sign Up to like & getrecommendations! Published in 2017 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnx230
Abstract: We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure… read more here.
Keywords: vector; quantization; vector bundles; lagrangian subvarieties ... See more keywords