Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel[1]; Stefan Müller-Stach[2]

  • [1] CIMAT Guanajuato, Mexico (Mexique)
  • [2] Johannes Gutenberg–Universität Mainz Institut für Mathematik Fachbereich 08 (Deutschland)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 6, page 2075-2085
  • ISSN: 0373-0956

Abstract

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We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

How to cite

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del Angel, Pedro Luis, and Müller-Stach, Stefan. "Differential Equations associated to Families of Algebraic Cycles." Annales de l’institut Fourier 58.6 (2008): 2075-2085. <http://eudml.org/doc/10370>.

@article{delAngel2008,
abstract = {We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.},
affiliation = {CIMAT Guanajuato, Mexico (Mexique); Johannes Gutenberg–Universität Mainz Institut für Mathematik Fachbereich 08 (Deutschland)},
author = {del Angel, Pedro Luis, Müller-Stach, Stefan},
journal = {Annales de l’institut Fourier},
keywords = {Higher Chow group; Picard-Fuchs operator; normal function; differential equation; higher Chow group},
language = {eng},
number = {6},
pages = {2075-2085},
publisher = {Association des Annales de l’institut Fourier},
title = {Differential Equations associated to Families of Algebraic Cycles},
url = {http://eudml.org/doc/10370},
volume = {58},
year = {2008},
}

TY - JOUR
AU - del Angel, Pedro Luis
AU - Müller-Stach, Stefan
TI - Differential Equations associated to Families of Algebraic Cycles
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 6
SP - 2075
EP - 2085
AB - We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.
LA - eng
KW - Higher Chow group; Picard-Fuchs operator; normal function; differential equation; higher Chow group
UR - http://eudml.org/doc/10370
ER -

References

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