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We study the generic linearly normal special scroll of genus g in P N . Moreover, we give a complete classification of the linearly normal scrolls in P 3 of genus 2 and 3. 相似文献
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We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Theorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in PN. Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Let G be a semisimple and simply connected algebraic group, and let H 0 be the subgroup of points fixed by an involution of G. Let V be an irreducible representation of G with a nonzero vector v fixed by H 0. In this article, we prove a property of the normalization of the coordinate ring of the closure of G·[v] in ?(V). 相似文献
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We classify the singularities of a surface ruled by conics: they are rational double points of type A n or D n . This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by conics. We determine also the family of such surfaces which are birational models of a given surface ruled by conics and obtained in a “minimal way” from it. 相似文献
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Any algebraic surface in which is fibered in cubics, so that the generic fibre is a twisted cubic, gives rise to a curve Γ in a suitable compactification
X of the space of smooth rational cubics of In this paper the case n = 4 is addressed and the corresponding space X is studied. We apply our results to complete the classification of smooth, rational surfaces in ruled in cubics.
This work is within the framework of the national research project “Geometry on Algebraic Varieties” Cofin 2006 of MIUR. 相似文献
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Ａ Ｃｌａｓｓ ｏｆ Ｍｕｌｔｉｓｉｄｅｄ Ｓｕｒｆａｃｅ ＰａｔｃｈｅｓＬｉｕＳｈｕｘｉｎ（刘树信）；ＸｉｎｇＬｉｐｉｎｇ（邢丽萍）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈａｎ，１３００２３）... 相似文献
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R. J. Higgs 《代数通讯》2017,45(10):4275-4282
There are many necessary and su?cient conditions on a finite group G to be abelian, for example, G contains no non-trivial commutators or that χ(1) = 1 for all χ∈Irr(G). Here an investigation is instigated into what remains of some of these conditions when a non-trivial 2-cocycle of G and the corresponding irreducible projective characters are considered instead, such as these characters all having the same degree. The conditions no longer imply, in general, that G is abelian, but it is conjectured that they do, at least, imply that G is solvable and some evidence is produced to support this view. 相似文献
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We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence. 相似文献
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Paltin Ionescu 《代数通讯》2013,41(12):5088-5094
In classical projective algebraic geometry, ?n was seen mainly as a linear subspace. The modern setting has produced in the last 40 years several remarkable abstract characterizations of projective space. We survey some interaction between these two points of view. 相似文献
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We show that any ruled minimal surface in the Berger sphere is a helicoid whose axis is a Hopf fiber by solving the ruled minimal surface equation in the parametric form. 相似文献
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Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and topologically simpler, including also Boy surface (real projective plane), using a family of ruled surfaces. We show their usefulness in visualizing the process using commonly available modeling software. 相似文献
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