共查询到20条相似文献,搜索用时 62 毫秒
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Beatriz Pascual-Escudero 《Journal of Pure and Applied Algebra》2019,223(6):2598-2614
Let X be an algebraic variety defined over a field of characteristic zero, and let be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in . More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in . 相似文献
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Let G be a reductive group scheme of type A acting on a spherical scheme X. We prove that there exists a number C such that the multiplicity is bounded by C, for any finite field F and any irreducible representation ρ of . We give an explicit bound for C. We conjecture that this result is true for any reductive group scheme and when F ranges (in addition) over all local fields of characteristic 0.Different aspects of this conjecture were studied in [3], [11], [6], [7]. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(10):107074
For a commutative ring A we consider a related graph, , whose vertices are the unimodular rows of length 2 up to multiplication by units. We prove that is path-connected if and only if A is a -ring, in the terminology of P. M. Cohn. Furthermore, if denotes the clique complex of , we prove that is simply connected if and only if A is universal for . More precisely, our main theorem is that for any commutative ring A the fundamental group of is isomorphic to the group modulo the subgroup generated by symbols. 相似文献
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Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on can be approximated uniformly on bounded sets by polyhedral norms and smooth norms, with arbitrary precision. We extend this result to more classes of spaces having uncountable symmetric bases, such as preduals of the ‘discrete’ Lorentz spaces , and certain symmetric Nakano spaces and Orlicz spaces. We also show that, given an arbitrary ordinal number α, there exists a scattered compact space K having Cantor–Bendixson height at least α, such that every equivalent norm on can be approximated as above. 相似文献
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Guram Bezhanishvili Nick Bezhanishvili Joel Lucero-Bryan Jan van Mill 《Annals of Pure and Applied Logic》2019,170(5):558-577
For a topological space X, let be the modal logic of X where □ is interpreted as interior (and hence ◇ as closure) in X. It was shown in [3] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, (), and their intersections arise as for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer to [3, Question 6.2]. On the other hand, we show that a scattered Stone space that is in addition hereditarily paracompact does not give rise to a new logic; namely we show that the logic of such a space is either S4.Grz or for some . In fact, we prove this result for any scattered locally compact open hereditarily collectionwise normal and open hereditarily strongly zero-dimensional space. 相似文献
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