# Quantization of canonical cones of algebraic curves

Benjamin Enriquez^{[1]}; Alexander Odesskii^{[2]}

- [1] Université Louis Pasteur, IRMA, 7 rue René Descartes, 67084 Strasbourg Cedex (France)
- [2] Landau Institute of Theoretical Physics, 2 Kosygina str., 117334 Moscow (Russie)

Annales de l’institut Fourier (2002)

- Volume: 52, Issue: 6, page 1629-1663
- ISSN: 0373-0956

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topEnriquez, Benjamin, and Odesskii, Alexander. "Quantization of canonical cones of algebraic curves." Annales de l’institut Fourier 52.6 (2002): 1629-1663. <http://eudml.org/doc/116022>.

@article{Enriquez2002,

abstract = {We introduce a quantization of the graded algebra of functions on the canonical cone of
an algebraic curve $C$, based on the theory of formal pseudodifferential operators. When
$C$ is a complex curve with Poincaré uniformization, we propose another, equivalent
construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a
presentation of the quantum algebra when $C$ is a rational curve, and discuss the problem
of constructing algebraically “differential liftings”.},

affiliation = {Université Louis Pasteur, IRMA, 7 rue René Descartes, 67084 Strasbourg Cedex (France); Landau Institute of Theoretical Physics, 2 Kosygina str., 117334 Moscow (Russie)},

author = {Enriquez, Benjamin, Odesskii, Alexander},

journal = {Annales de l’institut Fourier},

keywords = {algebraic curves; canonical cones; formal pseudodifferential operators; Rankin-Cohen brackets; Poincaré uniformization},

language = {eng},

number = {6},

pages = {1629-1663},

publisher = {Association des Annales de l'Institut Fourier},

title = {Quantization of canonical cones of algebraic curves},

url = {http://eudml.org/doc/116022},

volume = {52},

year = {2002},

}

TY - JOUR

AU - Enriquez, Benjamin

AU - Odesskii, Alexander

TI - Quantization of canonical cones of algebraic curves

JO - Annales de l’institut Fourier

PY - 2002

PB - Association des Annales de l'Institut Fourier

VL - 52

IS - 6

SP - 1629

EP - 1663

AB - We introduce a quantization of the graded algebra of functions on the canonical cone of
an algebraic curve $C$, based on the theory of formal pseudodifferential operators. When
$C$ is a complex curve with Poincaré uniformization, we propose another, equivalent
construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a
presentation of the quantum algebra when $C$ is a rational curve, and discuss the problem
of constructing algebraically “differential liftings”.

LA - eng

KW - algebraic curves; canonical cones; formal pseudodifferential operators; Rankin-Cohen brackets; Poincaré uniformization

UR - http://eudml.org/doc/116022

ER -

## References

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