1,720,972 research outputs found
Comparing powers and symbolic powers of ideals
No full textWe develop tools to study the problem of containment of symbolic powers I^(m) in powers I^r for a homogeneous ideal I in a polynomial ring k[PN] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I^(m) is contained in I^r. As corollaries, we show that I^2 contains I^(3) whenever S is a finite generic set of points in P^2 (thereby giving a partial answer to a question of Huneke), and we show that the containment theorems of Ein-Lazarsfeld-Smith [Invent. Math. 144 (2001), pp. 241-252] and Hochster-Huneke [Invent. Math. 147 (2002), pp. 349-369] are optimal for every fixed dimension and codimension
The resurgence of ideals of points and the containment problem
No full textWe relate properties of linear systems on X to the question of when I^r contains I^(m) in the case that I is the homogeneous ideal of a finite set of distinct points p_1,...,p_n in P^2, where X is the surface obtained by blowing up the points. We obtain complete answers for when I^r contains I^(m) when the points p_i's lie on a smooth conic or when the points are general and n ≤ 9
Containment results for ideals of various configurations of points in P^N
No full textGuided by evidence coming from a few key examples and attempting to unify previous work of Chudnovsky, Esnault-Viehweg, Eisenbud-Mazur, Ein-Lazarsfeld-Smith, Hochster-Huneke and Bocci-Harbourne, Harbourne and Huneke recently formulated a series of conjectures that relate symbolic and regular powers of ideals of fat points in PN. In this paper we propose another conjecture along the same lines, and we verify it and the conjectures of Harbourne and Huneke for a variety of configurations of points. The research that led to the present paper was partially supported by a grant of the group GNSAGA of INdAM
Projectively Normal but Superabundant Embeddings of Rational Surfaces in Projective Space
No full textPeuliar embeddings of certain rational surfaces are studied which are projectively normal, but the liner system adopted is superabundan
Expecting the unexpected: Quantifying the persistence of unexpected hypersurfaces
Full text linkThe independence of imposed vanishing conditions is a foundational issue for a wide range of research in algebraic geometry. In this spirit, if X⊂Pn is a reduced subscheme, we say that X admits an unexpected hypersurface of degree t and multiplicity m if requiring multiplicity m at a general point P fails to impose the expected number of conditions on the linear system of hypersurfaces of degree t containing X. Conditions which either guarantee the occurrence of unexpected hypersurfaces, or which ensure that they cannot occur, are not well understood. Research to date has made surprising connections to root systems, hyperplane arrangements, and generic splitting types of vector bundles, among other diverse topics. In this paper we introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We also exhibit algebraic and geometric properties of X which in some cases guarantee and in other cases preclude X having certain kinds of unexpectedness. In addition, we formulate a new way of quantifying unexpectedness (our AV sequence), which allows us to detect the extent to which unexpectedness persists as t increases but t−m remains constant. Finally, we study to what extent we can detect unexpectedness from the Hilbert function of X
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On the Classification of Certain Geproci Sets
Full text linkIn this short note we develop new methods toward the ultimate goal of classifying geproci sets in P3. We apply these methods to show that among sets of 16 points distributed evenly on 4 skew lines, up to projective equivalence there are only two distinct geproci sets. We give different geometric distinctions between these sets. The methods we develop here can be applied in a more general set-up; this is
the context of follow-up work [2]
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