{"type":"journal_article","date_created":"2026-07-07T06:18:00Z","abstract":[{"text":"<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>","lang":"eng"}],"publication":"Communications in Mathematical Physics","issue":"5","doi":"10.1007/s00220-025-05267-9","language":[{"iso":"eng"}],"article_number":"97","intvolume":"       406","publication_status":"published","date_updated":"2026-07-07T06:18:58Z","author":[{"full_name":"Burban, Igor","first_name":"Igor","last_name":"Burban","id":"72064"},{"last_name":"Klevtsov","first_name":"Semyon","full_name":"Klevtsov, Semyon"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]},"title":"Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus","year":"2025","citation":{"chicago":"Burban, Igor, and Semyon Klevtsov. “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus.” <i>Communications in Mathematical Physics</i> 406, no. 5 (2025). <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">https://doi.org/10.1007/s00220-025-05267-9</a>.","short":"I. Burban, S. Klevtsov, Communications in Mathematical Physics 406 (2025).","apa":"Burban, I., &#38; Klevtsov, S. (2025). Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus. <i>Communications in Mathematical Physics</i>, <i>406</i>(5), Article 97. <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">https://doi.org/10.1007/s00220-025-05267-9</a>","ieee":"I. Burban and S. Klevtsov, “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, Art. no. 97, 2025, doi: <a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>.","ama":"Burban I, Klevtsov S. Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus. <i>Communications in Mathematical Physics</i>. 2025;406(5). doi:<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>","bibtex":"@article{Burban_Klevtsov_2025, title={Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus}, volume={406}, DOI={<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>}, number={597}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Burban, Igor and Klevtsov, Semyon}, year={2025} }","mla":"Burban, Igor, and Semyon Klevtsov. “Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, 97, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05267-9\">10.1007/s00220-025-05267-9</a>."},"volume":406,"user_id":"72064","_id":"66291","publisher":"Springer Science and Business Media LLC","status":"public"}