1,720,972 research outputs found
On the algebraicity of the zero locus of an admissible normal function
No full textWe show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic. In Part II of the paper, which is an appendix, we compute the Tannakian Galois group of the category of one-variable admissible real nilpotent orbits with split limit. We then use the answer to recover an unpublished theorem of Deligne, which characterizes the sl2-splitting of a real mixed Hodge structure. © © The Author(s) 2013
-orbits and degenerations of mixed Hodge structure
No full textWe extend Schmid’s SL2-orbit theorem to a class of variations of mixed Hodge structure which normal functions, logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as a consequence of this theorem, we obtain a simple formula for the asymptotic behavior of the archimedean height of a flat family of algebraic cycles which depends only on the weight filtration and local monodromy. © 2006 Applied Probability Trust
Boundary components of mumford-tate domains
No full textWe study certain spaces of nilpotent orbits in Hodge domains, and we treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these spaces as iteratively fibered algebraic-group orbits in a minimal way
Jumps in the archimedean height
No full textWe introduce a pairing on local intersection cohomology groups of variations of pure Hodge structure, which we call the asymptotic height pairing. Our original application of this pairing was to answer a question on the Ceresa cycle posed by R. Hain and D. Reed. (This question has since been answered independently by Hain.) Here we show that a certain analytic line bundle, called the biextension line bundle, and defined in terms of normal functions, always extends to any smooth partial compactification of the base. We then show that the asymptotic height pairing on intersection cohomology governs the extension of the natural metric on this line bundle studied by Hain and Reed (as well as, more recently, by several other authors). We also prove a positivity property of the asymptotic height pairing, which generalizes the results of a recent preprint of J. Burgos Gil, D. Holmes and R. de Jong, along with a continuity property of the pairing in the normal function case. Moreover, we show that the asymptotic height pairing arises in a natural way from certain Mumford–Grothendieck biextensions associated to normal functions
Naive boundary strata and nilpotent orbits
No full textWe give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups SU(2, 1), Sp4, and G2
Variations of mixed Hodge structure, Higgs fields, and quantum cohomology
No full textFollowing C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over Q carries a natural Higgs bundle structure ∂ + θ which is invariant under the C* action studied in [20]. We then specialize our construction to the context of [6], and show that the resulting Higgs field θ determines (and is determined by) the Gromov-Witten potential of the underlying family of Calabi-Yau threefolds
Zero loci of admissible normal functions With torsion singularities
No full textWe show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to an admissible normal function on a smooth compactification such that the divisor at infinity is also smooth. This result, which has also been obtained recently by M. Saito using a different method [22], generalizes a previous result proved by the authors for admissible normal functions on curves [4]. © 2009
Asymptotics of degenerations of mixed Hodge structures
No full textWe construct a hermitian metric on the classifying spaces of graded-polarized mixed Hodge structures and prove analogs of the strong distance estimate [6] between an admissible period map and the approximating nilpotent orbit. We also consider the asymptotic behavior of the biextension metric introduced by Hain [12], analogs of the norm estimates of [19] and the asymptotics of the naive limit Hodge filtration considered in [21]
The zero locus of an admissible normal function
No full textWe prove that the zero locus of an admissible normal function over an algebraic parameter space S is algebraic in the case where S is a curve
Degenerations of mixed Hodge structure
Get PDFWe extend certain aspects of C. Simpson's correspondence between harmonic metrics and variations of Hodge structure to the category of complex variations of mixed Hodge structure, and we prove an analog of W. Schmid's nilpotent orbit theorem for admissible variations of graded-polarized mixed Hodge structure
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