Global Euler obstruction and polar invariants

Let be a purely dimensional, complex algebraic singular space. We define a global Euler obstruction Eu(Y) which extends the Euler-Poincaré characteristic in case of a nonsingular Y. Using Lefschetz pencils, we express Eu(Y) as alternating sum of global polar invariants. Partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401.     

Performance of Nd:YLF laser by using crystal electrooptic Q-switch

The polarization rotating coefficient and the laser-damage threshold of La₃Ga₅SiO₁₄ crystal at 1064 nm are measured, which are 1.1 deg/mm and , respectively. The working principle and the design method of electrooptic Q-switch based on La₃Ga₅SiO₁₄ crystal, which has the optical activity, are reported. The performance of Nd:YLF laser with the electrooptic Q-switch of La₃Ga₅SiO₁₄ crystal was studied. The output pulses with an energy of 379 mJ, a duration of 8.7 ns and repetition of 10 Hz are achieved.     

Torsion cohomology classes and algebraic cycles on complex projective manifolds

Atiyah and Hirzebruch gave examples of even degree torsion classes in the singular cohomology of a smooth complex projective manifold, which are not Poincaré dual to an algebraic cycle. We notice that the order of these classes must be small compared to the dimension of the manifold. However, building upon a construction of Kollár, one can provide such examples with arbitrary high prime order, the dimension being fixed. This method also provides examples of torsion algebraic cycles, which are non trivial in the Griffiths group, and lie in a arbitrary high level of the H. Saito filtration on Chow groups.     

Gated sets in metric spaces

The concept of a gated subset in a metric space is studied, and it is shown that properties of disjoint pairs of gated subsets can be used to investigate projections in Tits buildings.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

The Farahat-Higman ring of wreath products and Hilbert schemes

We study the structure constants of the class algebra of the wreath products Γ_n associated to an arbitrary finite group Γ with respect to the basis of conjugacy classes. We show that a suitable filtration on gives rise to the graded ring with non-negative integer structure constants independent of n (some of which are computed), which are then encoded in a Farahat-Higman ring 14" border="0" style="vertical-align:bottom" width="22" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0001870803002834-si4.gif">. The real conjugacy classes of Γ come to play a distinguished role and are treated in detail in the case when Γ is a subgroup of . The above results provide new insight to the cohomology rings of Hilbert schemes of points on a quasi-projective surface X.     

Castelnuovo-Mumford regularity for nonhyperelliptic curves

The purpose here is to show that an irreducible, reduced, projective, nonhyperelliptic curve of degree d and genus g is n-regular for if Received: 10 July 2003