Sur les surfaces lisses de ℙ4

Sans résuméEspace projectif sur un corps algébriquement clos de caractéristique zéro     

Stable rank-2 vector bundles on ℙ3 withc 1=0 andc 2=3

Mathematische Annalen -     

An intersection number for the punctual Hilbert scheme of a surface

We compute the intersection number between two cycles and of complementary dimensions in the Hilbert scheme parameterizing subschemes of given finite length of a smooth projective surface . The -cycle corresponds to the set of finite closed subschemes the support of which has cardinality 1. The -cycle consists of the closed subschemes the support of which is one given point of the surface. Since is contained in , indirect methods are needed. The intersection number is , answering a question by H. Nakajima.

     

Irreducibility of the punctual quotient scheme of a surface

It is shown that the punctual quotient schemeQ _l ^r parametrizing all zero-dimensional quotients of lengthl and supported at some fixed point O∈A ² in the plane is irreducible.     

Bott's formula and enumerative geometry

We outline a strategy for computing intersection numbers on
smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed. The results are consistent with predictions made from mirror symmetry computations. We also compute degrees of some loci in the linear system of plane curves of degrees less than 10, like those corresponding to sums of powers of linear forms, and curves carrying inscribed polygons.

     

Torsional dynamics of the Birnboim-Schrag multiple lump resonator studied using TV-holography

We have studied the torsional dynamics of the Birnboim-Schrag multiple lump resonator (MLR) using TV holography. The relative torsional displacement amplitudes have been determined for all resonator lumps at their five resonance modes. Due to the low vibration amplitudes for the highest frequency mode, we only give a rough estimate of the relative torsional displacements for this resonance. For some lumps, the observed relative displacement amplitudes deviate by as much as a factor of 2 from the predictions of the dumbbell theory commonly used to analyze MLR dynamics. The experimental data agree well with the recent theoretical analysis carried out by Mikkelsen et al. (1992).