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1.
In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in
, the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in
. 相似文献
2.
对于任意的正数M以及正整数d≥4,存在直径为d的i-边连通无环图G使得ζ(G)≥M,其中ζ(G)是G的Betti亏数,i=1,2,3。 相似文献
3.
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of -power degrees with class numbers equal to their genus class numbers.
4.
We describe an algorithm for the dominating set problem with time complexity O((4g+40)kn2) for graphs of bounded genus g1, where k is the size of the set. It has previously been shown that this problem is fixed parameter tractable for planar graphs. We give a simpler proof for the previous O(8kn2) result for planar graphs. Our method is a refinement of the earlier techniques. 相似文献
5.
Recently Bezerra, Garcia and Stichtenoth constructed an explicit tower F=(Fn)n?0 of function fields over a finite field Fq3, whose limit λ(F)=limn→∞N(Fn)/g(Fn) attains the Zink bound λ(F)?2(q2−1)/(q+2). Their proof is rather long and very technical. In this paper we replace the complex calculations in their work by structural arguments, thus giving a much simpler and shorter proof for the limit of the Bezerra, Garcia and Stichtenoth tower. 相似文献
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9.
The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from 2 this theorem is extended here to function fields of conics. The main result is that there is at most one extension of a valuation on the base field to the function field of a conic for which the residue field extension is transcendental but not ruled. Furthermore the situation when this valuation is present is characterised. 相似文献
10.
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numbers occur in the enumeration of fibered achiral and unknotting number one rational knots. Then we show how to enumerate rational knots of given crossing number depending on genus and/or signature. This allows to determine the asymptotical average value of these invariants among rational knots. We give also an application to the enumeration of lens spaces. 相似文献