Differential Equations associated to Families of Algebraic Cycles
Annales de l'Institut Fourier, Volume 58 (2008) no. 6, p. 2075-2085

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.

Nous développons une théorie d’équations associées aux familles de cycles algébriques dans des groupes de Chow supérieurs. Ce formalisme est lié au type inhomogène d’équations de Picard-Fuchs. Pour les familles de surfaces K3 l’équation différentielle ordinaire non-linéaire est semblable à l’équation de Chazy.

DOI : https://doi.org/10.5802/aif.2406
Classification:  14C25,  19E20
Keywords: Higher Chow group, Picard-Fuchs operator, normal function, differential equation
@article{AIF_2008__58_6_2075_0,
     author = {del Angel, Pedro Luis and M\"uller-Stach, Stefan},
     title = {Differential Equations associated to Families of Algebraic Cycles},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {6},
     year = {2008},
     pages = {2075-2085},
     doi = {10.5802/aif.2406},
     mrnumber = {2473629},
     zbl = {1151.14009},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_6_2075_0}
}
del Angel, Pedro Luis; Müller-Stach, Stefan. Differential Equations associated to Families of Algebraic Cycles. Annales de l'Institut Fourier, Volume 58 (2008) no. 6, pp. 2075-2085. doi : 10.5802/aif.2406. http://www.numdam.org/item/AIF_2008__58_6_2075_0/

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