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In this note we are interested in the graded modulesM
k=I(k)/Ik and
, whereI is a saturated ideal in the homogeneous coordinate ringS=K[x0,…,xn] of ℙn,I
(k) is the symbolic power and
is the saturation of the ordinary power. Very little is known about these modules, and we provide a bound on their diameters,
we compute the Hilbert functions and we study some characteristic submodules in the special case ofn+1 general points in ℙn.
Sunto In questa nota siamo interessati ai moduli graduatiM k=I(k)/Ik e , doveI è un ideale saturato nell'anello delle coordinate omogeneeS:=K[x0,…,xn] di ℙn,I (k) è la potenza simbolica e è la saturazione della potenza ordinaria. Poco è noto su questi moduli e qui viene fornito un limite superiore ai loro diametri. Ne calcoliamo inoltre le funzioni di Hilbert e studiamo alcuni sottomoduli caratteristici nel caso speciale din+1 punti in posizione generale, in ℙn.相似文献
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Jon Eivind Vatne 《Mathematische Nachrichten》2008,281(3):434-441
There are very many non‐reduced schemes. In this paper, we consider two examples to back this statement: we give lists of double scheme structures on a twisted cubic, and we construct rank two bundles on projective 3‐space with prescribed Chern classes, from double structures on smooth rational curves. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Jon Eivind Vatne 《Annali dell'Universita di Ferrara》2012,58(1):199-215
In this paper we study Cohen–Macaulay monomial multiple structures (non-reduced schemes) on a linear subspace of codimension
two in projective space. We show that these structures determine smooth points in their respective Hilbert schemes, with (smooth)
neighbourhoods of two such points intersecting if their Hilbert functions are equal. We generalize a construction for multiple
structures on points in the plane to this setting, giving a kind of product of monomial multiple structures. For points, this
construction can be found in Nakajima’s book (Lectures on Hilbert schemes of points on surfaces, Univ Lecture Ser AMS, vol
18, 1999). The tools we use for studying multiple structures are developed in Vatne (Math Nachr 281(3):434–441, 2008; Comm Algebra 37(11):3861–3873, 2009) (see also Vatne in Towards a classification of multiple structures, PhD thesis, University of Bergen, 2001). 相似文献
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We generalise the notion of cluster structures from the work of Buan–Iyama–Reiten–Scott to include situations where the endomorphism rings of the clusters may have loops.
We show that in a Hom-finite 2-Calabi–Yau category, the set of maximal rigid objects satisfies these axioms whenever there
are no 2-cycles in the quivers of their endomorphism rings. We apply this result to the cluster category of a tube, and show
that this category forms a good model for the combinatorics of a type B cluster algebra. 相似文献
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Jon Eivind Vatne 《Applications of Mathematics》2017,62(3):213-223
Acute triangles are defined by having all angles less than π/2, and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension n ≥ 3, acuteness is defined by demanding that all dihedral angles between (n?1)-dimensional faces are smaller than π/2. However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property of acuteness is logically independent of the property of containing the circumcenter when the dimension is greater than two. In this article, we show that the latter property is also quite rare in higher dimensions. In a natural probability measure on the set of n-dimensional simplices, we show that the probability that a uniformly random n-simplex contains its circumcenter is 1/2 n . 相似文献
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