PEDRO DEL ANGEL - Academia.edu (original) (raw)
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Papers by PEDRO DEL ANGEL
arXiv (Cornell University), Nov 2, 2009
We use L 2-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H 1 (S, j ... more We use L 2-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H 1 (S, j * V), where the local system V arises from the third primitive cohomology of family of Calabi-Yau threefolds over a curveS. The method gives a way to predict the presence of algebraic 2-cycles in the total space of the family and is applied to some examples.
Annales de l’institut Fourier, 2008
We develop a theory of differential equations associated to families of algebraic cycles in highe... more 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 families of K3 surfaces the corresponding non-linear ODE turns out to be similar to Chazy's equation.
arXiv (Cornell University), Aug 7, 2018
The normal function associated to algebraic cycles in higher Chow groups defines a differential e... more The normal function associated to algebraic cycles in higher Chow groups defines a differential equation. This Picard-Fuchs equation defines an extension of D-modules as well as an extension of local systems. In this paper, we show that both extensions define the same extension of mixed Hodge modules determined by the normal function.
Calabi-Yau Varieties and Mirror Symmetry, 2003
This paper continues the work done in [9] and is an attempt to establish a conceptual framework w... more This paper continues the work done in [9] and is an attempt to establish a conceptual framework which generalizes the work of Manin [21] on the relation between non-linear second order ODE of type Painlevé VI and integrable systems. The principle behind everything is a strong interaction between K-theory and Picard-Fuchs type differential equations via Abel-Jacobi maps. Our main result is an extension of a theorem of Donagi and Markman [12].
arXiv (Cornell University), Nov 2, 2009
We use L 2-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H 1 (S, j ... more We use L 2-Higgs cohomology to determine the Hodge numbers of the parabolic cohomology H 1 (S, j * V), where the local system V arises from the third primitive cohomology of family of Calabi-Yau threefolds over a curveS. The method gives a way to predict the presence of algebraic 2-cycles in the total space of the family and is applied to some examples.
Annales de l’institut Fourier, 2008
We develop a theory of differential equations associated to families of algebraic cycles in highe... more 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 families of K3 surfaces the corresponding non-linear ODE turns out to be similar to Chazy's equation.
arXiv (Cornell University), Aug 7, 2018
The normal function associated to algebraic cycles in higher Chow groups defines a differential e... more The normal function associated to algebraic cycles in higher Chow groups defines a differential equation. This Picard-Fuchs equation defines an extension of D-modules as well as an extension of local systems. In this paper, we show that both extensions define the same extension of mixed Hodge modules determined by the normal function.
Calabi-Yau Varieties and Mirror Symmetry, 2003
This paper continues the work done in [9] and is an attempt to establish a conceptual framework w... more This paper continues the work done in [9] and is an attempt to establish a conceptual framework which generalizes the work of Manin [21] on the relation between non-linear second order ODE of type Painlevé VI and integrable systems. The principle behind everything is a strong interaction between K-theory and Picard-Fuchs type differential equations via Abel-Jacobi maps. Our main result is an extension of a theorem of Donagi and Markman [12].