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On a smooth curve a theta-characteristic is a line bundle L,the square of which is the canonical line bundle . The equivalentcondition om(L, ) L generalizes well to singular curves, asapplications show. More precisely, a theta-characteristic isa torsion-free sheaf of rank 1 with om(, ) . If the curvehas non-ADE singularities, then there are infinitely many theta-characteristics.Therefore, theta-characteristics are distinguished by theirlocal type. The main purpose of this article is to compute thenumber of even and odd theta-characteristics (that is withh0(C, ) 0 and h0(C, ) 1 modulo 2, respectively) in terms ofthe geometric genus of the curve and certain discrete invariantsof a fixed local type. 相似文献
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My master thesis concerns the solution linear complementarity problems (LCP). The Lemke algorithm, the most commonly used algorithm for solving a LCP until this day, was compared with the piecewise Newton method (PLN algorithm). The piecewise Newton method is an algorithm to solve a piecewise linear system on the basis of damped Newton methods. The linear complementarity problem is formulated as a piecewise linear system for the applicability of the PLN algorithm. Then, different application examples will be presented, solved with the PLN algorithm. As a result of the findings (of my master thesis) it can be assumed that – under the condition of coherent orientation – the PLN-algorithm requires fewer iterations to solve a linear complementarity problem than the Lemke algorithm. The coherent orientation for piecewise linear problems corresponds for linear complementarity problems to the P-matrix-property. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Jens Piontkowski 《manuscripta mathematica》1996,89(1):79-85
The purpose of this paper is to give an elementary proof of Griffiths' and Harris' normal form lemma [4, p.385].
The author thanks Gerd Fischer for his encouragement and support
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
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Jens Piontkowski 《Mathematische Zeitschrift》2007,255(1):195-226
We compute the Euler number of the compactified Jacobian of a curve whose minimal unibranched normalization has only plane irreducible singularities with characteristic Puiseux exponents (p, q), (4, 2q, s), (6, 8, s), or (6, 10, s). Further, we derive a combinatorial method to compute the Betti numbers of the compactified Jacobian of an unibranched rational curve with singularities like above. Some of the Betti numbers can be stated explicitly. 相似文献
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Jens Piontkowski 《Journal of Pure and Applied Algebra》2006,207(2):327-339
Let C be a reduced curve singularity. C is called of finite self-dual type if there exist only finitely many isomorphism classes of indecomposable, self-dual, torsion-free modules over the local ring of C. In this paper it is shown that the singularities of finite self-dual type are those which dominate a simple plane singularity. 相似文献
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Jens Piontkowski 《manuscripta mathematica》2001,106(1):75-99
A projective variety is called developable if the image of its Gauss map has a smaller dimension than the variety itself.
Developable varieties are always singular, and requiring that all singularities lie in a hyperplane puts a severe restriction
on them. Here we refine a theorem of Wu and Zheng stating that such varieties are the union of cones if the dimension of the
Gauss image is less than or equal to four. Afterwards we study their singular locus. Finally, we describe the geometry of
such varieties whose Gauss image has dimension two.
Received: Received: 8 November 2000 / Revised version: 15 May 2001 相似文献
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