共查询到20条相似文献,搜索用时 15 毫秒
1.
Marina Mancini 《Annali dell'Universita di Ferrara》1999,45(1):163-175
In this paper we study the embeddings of smallest degree of a generic curveC of genusg as a projectively normal curve.
Sunto In questo articolo studiamo le immersioni di grado minimo di una generica curvaC di genereg come curva proiettivamente normale.相似文献
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Axel Kohnert 《Annals of Combinatorics》1997,1(1):367-375
Schur polynomials are a special case of Schubert polynomials. In this paper, we give an algorithm to compute the product of
a Schubert polynomial with a Schur polynomial on the basis of Schubert polynomials. This is a special case of the general
problem of the multiplication of two Schubert polynomials, where the corresponding algorithm is still missing. The main tools
for the given algorithm is a factorization property of a special class of Schubert polynomials and the transition formula
for Schubert polynomials. 相似文献
3.
Laura Bazzotti 《Journal of Pure and Applied Algebra》2006,207(2):319-326
For a finite set of points X⊆Pn and for a given point P∈X, the notion of a separator of P in X (a hypersurface containing all the points in X except P) and of the degree of P in X, (the minimum degree of these separators) has been largely studied. In this paper we extend these notions to a set of points X on a projectively normal surface S⊆Pn, considering as separators arithmetically Cohen-Macaulay curves and generalizing the case S=P2 in a natural way. We denote the minimum degree of such curves as and we study its relation to . We prove that if S is a variety of minimal degree these two terms are explicitly related by a formula, whereas only an inequality holds for other kinds of surfaces. 相似文献
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Kiumars Kaveh Christopher Manon Takuya Murata 《Journal of Pure and Applied Algebra》2021,225(11):106713
We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra R over an algebraically closed field k. Building on work of Römer and Schmitz, we give a formula for each initial ideal, and we express the associated quasivaluations in terms of certain I-adic filtrations. As a corollary, we show that in the case that R is a domain, every initial ideal coming from the codimension 1 skeleton of the tropical variety is prime, so “generic presentations of Cohen-Macaulay domains are well-poised in codimension 1.” 相似文献
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Takeshi Kajiwara 《Archiv der Mathematik》2006,86(1):43-49
We show fundamental properties on embedding of abelian surfaces into projective toric 4-folds, and study the case of the toric
Del Pezzo 4-fold from the viewpoint of the moduli space of abelian surfaces with polarization of type (1, 5).
Received: 31 January 2005; revised: 15 April 2005 相似文献
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Indranil Biswas 《Indagationes Mathematicae》2005,16(1):1-19
Let G be a connected semisimple linear algebraic group defined over an algebraically closed field k and P ⊂ G a parabolic subgroup without any simple factor. Let H be a connected reductive linear algebraic group defined over the field k such that all the simple quotients of H are of classical type. Take any homomorphism π : P → H such that the image of p is not contained in any proper parabolic subgroup of H. Consider the corresponding principal H-bundle EP(H) = (G × H)/P over G/P. We prove that EP (H) is strongly stable with respect to any polarization on G/P. 相似文献
11.
Alana Huszar Steffen Marcus Martin Ulirsch 《Journal of Pure and Applied Algebra》2019,223(5):2036-2061
The classical clutching and gluing maps between the moduli stacks of stable marked algebraic curves are not logarithmic, i.e. they do not induce morphisms over the category of logarithmic schemes, since they factor through the boundary. Using insight from tropical geometry, we enrich the category of logarithmic schemes to include so-called sub-logarithmic morphisms and show that the clutching and gluing maps are naturally sub-logarithmic. Building on the recent framework developed by Cavalieri, Chan, Wise, and the third author, we further develop a stack-theoretic counterpart of these maps in the tropical world and show that the resulting maps naturally commute with the process of tropicalization. 相似文献
12.
We prove that the moduli spaces of rational curves of degree at most 3 in linear sections of the Grassmannian are all rational varieties. We also study their compactifications and birational geometry. 相似文献
13.
Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables. 相似文献
14.
The recursive nature of cominuscule Schubert calculus 总被引:1,自引:0,他引:1
The necessary and sufficient Horn inequalities which determine the non-vanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson coefficients on smaller Grassmannians. We show how non-vanishing in the Schubert calculus for cominuscule flag varieties is similarly recursive. For these varieties, the non-vanishing of products of Schubert classes is controlled by the non-vanishing products on smaller cominuscule flag varieties. In particular, we show that the lists of Schubert classes whose product is non-zero naturally correspond to the integer points in the feasibility polytope, which is defined by inequalities coming from non-vanishing products of Schubert classes on smaller cominuscule flag varieties. While the Grassmannian is cominuscule, our necessary and sufficient inequalities are different than the classical Horn inequalities. 相似文献
15.
We connect different results about irreducible components of the Springer fibers of type A. Firstly, we show a relation between the Spaltenstein partition of the fibers and a total order
on the set of standard Young tableaux. Next, using a result of Steinberg, we connect a work of the first author to the Robinson–Schensted
map. We also perform the Spaltenstein study of the relative position of the Springer fibers and
-fibrations of the flag manifold. This leads us to consider the adjacency relation on the set of standard Young tableaux
and to define oriented and labeled graphs with the standard Young tableaux as vertices. Using this adjacency relation, we
describe some smooth irreducible components of the Springer fibers. Finally, we show that these graphs can be identified with
some full subgraphs of the Bruhat graph. 相似文献
16.
Given a permutation , construct a graph G
π on the vertex set {1, 2,..., n} by joining i to j if (i) i < j and π(i) < π(j) and (ii) there is no k such that i < k < j and π(i) < π(k) < π(j). We say that π is forest-like if G
π is a forest. We first characterize forest-like permutations in terms of pattern avoidance, and then by a certain linear map
being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties
which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert
varieties).
We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then
adapt our method to count permutations for which G
π is a tree, or a path, and recover the known generating function of smooth permutations.
Received March 27, 2006 相似文献
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Mark Pankov 《Archiv der Mathematik》2007,89(1):81-86
Let H be a separable real Hilbert space. Denote by
(H) the Grassmannian consisting of closed subspaces with infinite dimension and codimension. This Grassmannian is partially
ordered by the inclusion relation. We show that every order preserving transformation of
(H) can be extended to an automorphism of the lattice of closed subspaces of H. It follows from Mackey’s result [8] that automorphisms of this lattice are induced by invertible bounded linear operators.
Dedicated to G. W. Mackey (1916–2006)
Received: 15 May 2006 Revised: 16 October 2006 相似文献