---
res:
  bibo_abstract:
  - "<jats:title>Abstract</jats:title>\r\n          <jats:p>In 1993 Keski-Vakkuri
    and Wen introduced a model for the fractional quantum Hall effect based on multilayer
    two-dimensional electron systems satisfying quasi-periodic boundary conditions.
    Such a model is essentially specified by a choice of a complex torus <jats:italic>E</jats:italic>
    and a symmetric positively definite matrix <jats:italic>K</jats:italic> of size
    <jats:italic>g</jats:italic> with non-negative integral coefficients, satisfying
    some further constraints. The space of the corresponding wave functions turns
    out to be <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\delta
    $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula>-dimensional, where <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\delta
    $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> is the determinant of <jats:italic>K</jats:italic>.
    We construct a hermitian holomorphic bundle of rank <jats:inline-formula>\r\n
    \             <jats:alternatives>\r\n                <jats:tex-math>$$\\delta
    $$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mi>δ</mml:mi>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> on the abelian variety <jats:italic>A</jats:italic>
    (which is the <jats:italic>g</jats:italic>-fold product of the torus <jats:italic>E</jats:italic>
    with itself), whose fibres can be identified with the space of wave function of
    Keski-Vakkuri and Wen. A rigorous construction of this “magnetic bundle” involves
    the technique of Fourier–Mukai transforms on abelian varieties. The constructed
    bundle turns out to be simple and semi-homogeneous and it can be equipped with
    two different (and natural) hermitian metrics: the one coming from the center-of-mass
    dynamics and the one coming from the Hilbert space of the underlying many-body
    system. We prove that the canonical Bott–Chern connection of the first hermitian
    metric is always projectively flat and give sufficient conditions for this property
    for the second hermitian metric.</jats:p>@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Igor
      foaf_name: Burban, Igor
      foaf_surname: Burban
      foaf_workInfoHomepage: http://www.librecat.org/personId=72064
  - foaf_Person:
      foaf_givenName: Semyon
      foaf_name: Klevtsov, Semyon
      foaf_surname: Klevtsov
  bibo_doi: 10.1007/s00220-025-05267-9
  bibo_issue: '5'
  bibo_volume: 406
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0010-3616
  - http://id.crossref.org/issn/1432-0916
  dct_language: eng
  dct_publisher: Springer Science and Business Media LLC@
  dct_title: Algebraic Geometry of the Multilayer Model of the Fractional Quantum
    Hall Effect on a Torus@
...