The Hodge conjecture for self-products of certain K3 surfaces

We use a result of van Geemen to determine the endomorphism algebra of the Kuga--Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of \PP^2 which are ramified along six lines.Comment: 24 page

Stability of tautological vector bundles on Hilbert squares of surfaces

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.Comment: 8 page

Erscheinungsjahr: 2009.

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Geometrically consistent elastic matching of 3D shapes: A linear programming solution

We propose a novel method for computing a geometri-cally consistent and spatially dense matching between two 3D shapes. Rather than mapping points to points we match infinitesimal surface patches while preserving the geomet-ric structures. In this spirit we consider matchings as dif-feomorphisms between the objects ’ surfaces which are by definition geometrically consistent. Based on the observa-tion that such diffeomorphisms can be represented as closed and continuous surfaces in the product space of the two shapes we are led to a minimal surface problem in this prod-uct space. The proposed discrete formulation describes the search space with linear constraints. Computationally, our approach leads to a binary linear program whose relaxed version can be solved efficiently in a globally optimal man-ner. As cost function for matching, we consider a thin shell energy, measuring the physical energy necessary to deform one shape into the other. Experimental results demonstrate that the proposed LP relaxation allows to compute high-quality matchings which reliably put into correspondence articulated 3D shapes. Moreover a quantitative evaluation shows improvements over existing works. 1