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Chris Peters

Publications and source records attributed to Chris Peters.

24 records · Page 2Linked to original sources
arXiv2009

Bloch-type conjectures and an example of a threefold of general type

The hypothetical existence of a good theory of mixed motives predicts many deep phenomena related to algebraic cycles. One of these, a generalization of Bloch's conjecture says that "small Hodge diamonds" go with "small Chow groups". Voisin's method (which produces examples with small Chow groups) is analyzed carefully to widen its applicability. A threefold of general type without 1- and 2-forms is exhibited for which this extension yields Bloch's generalized conjecture.

math.AG↗
arXiv2008

Lowest Weights in Cohomology of Variations of Hodge Structure (II)

Let $X$ be an irreducible complex analytic space with $j:U\into X$ an immersion of a smooth Zariski open subset, and let $\bV$ be a variation of Hodge structure of weight $n$ over $U$. Assume $X$ is compact Kähler. Then provided the local monodromy operators at infinity are quasi-unipotent, $IH^k(X, \bV)$ is known to carry a pure Hodge structure of weight $k+n$, while $H^k(U,\bV)$ carries a mixed Hodge structure of weight $\ge k+n$. In this note it is shown that the image of the natural map $IH^k(X,\bV) \to H^k(U,\bV)$ is the lowest weight part of this mixed Hodge structure. In the algebraic case this easily follows from the formalism of mixed sheaves, but the analytic case is rather complicated, in particular when the complement $X-U$ is not a hypersurface.

math.AG↗
arXiv2008

Automorphs of indefinite binary quadratic forms and K3-surfaces with Picard number 2

Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of automorphs for binary forms can then be applied to study these automorphism groups. The result is a precise description of all possible automorphism groups of ``general'' K3's with Picard number two.

math.AG↗
arXiv2007

Lowest Weights in Cohomology of Variations of Hodge Structure

Let X be a smooth complex projective variety, let $j:U\into X$ an immersion of a Zariski open subset, and let V be a variation of Hodge structure of weight n over U. Then IH^k(X, j_*V) is known to carry a pure Hodge structure of weight k+n, while H^k(U,V) carries a mixed Hodge structure of weight $\ge k+n$. In this note it is shown that the image of the natural map $IH^k(X,j_*V) \to H^k(U,V)$ is the lowest weight part of this mixed Hodge structure. The proof uses Saito's theory of mixed Hodge modules.

math.AG↗
arXiv2000

Arakelov-type inequalities for Hodge bundles

We give a proof of generalizations of the classical Arakelov inequality valid for the degree $d$ of the relative canoincal bundle of a family of curves of genus $g$ over a complete curve of genus $p$ under the assumption that the monodromy around the singular fibers is unipotent. This relative canonical bundle is the (canonical extension of) the Hodge bundle and the inequality is generalized to the degrees of the Hodge bundles of a complex variation of Hodge structures.

math.AG↗