共查询到20条相似文献,搜索用时 406 毫秒
2.
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root. 相似文献
3.
E. Yu. Smirnov 《Functional Analysis and Its Applications》2008,42(2):126-134
Let X = Gr(k, V) × Gr(l, V) be the direct product of two Grassmann varieties of k-and l-planes in a finite-dimensional vector space V, and let B ? GL(V) be the isotropy group of a complete flag in V. We consider B-orbits in X, which are an analog of Schubert cells in Grassmannians. We describe this set of orbits combinatorially and construct desingularizations for the closures of these orbits, similar to the Bott-Samelson desingularizations for Schubert varieties. 相似文献
4.
Izzet Coskun 《Israel Journal of Mathematics》2014,200(1):85-126
A Schubert class σ in the cohomology of a homogeneous variety X is called rigid if the only projective subvarieties of X representing σ are Schubert varieties. A Schubert class σ is called multi rigid if the only projective subvarieties representing positive integral multiples of σ are unions of Schubert varieties. In this paper, we discuss the rigidity and multi rigidity of Schubert classes in orthogonal Grassmannians. For a large set of non-rigid classes, we provide explicit deformations of Schubert varieties using combinatorially defined varieties called restriction varieties. We characterize rigid and multi rigid Schubert classes of Grassmannian and quadric type. We also characterize all the rigid classes in OG(2, n) if n > 8. 相似文献
5.
S. K. Pattanayak 《代数通讯》2013,41(9):3811-3822
For any simple, simply connected algebraic group G of exceptional types (E 6, E 7, E 8, F 4, and G 2) and for any maximal parabolic subgroup P of G, we describe all minimal (with respect to inclusion) Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. This completes the answer to a question proposed in [8] and settled there in the classical case. 相似文献
6.
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus. 相似文献
7.
Chuck Hague 《Journal of Algebra》2010,323(6):1758-1764
Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic. In this note, we show that an irreducible closed subvariety of the flag variety of G is compatibly split by the unique canonical Frobenius splitting if and only if it is a Richardson variety, i.e. an intersection of a Schubert and an opposite Schubert variety. 相似文献
8.
Cristian Lenart Frank Sottile 《Transactions of the American Mathematical Society》2007,359(5):2317-2342
We derive explicit Pieri-type multiplication formulas in the Grothendieck ring of a flag variety. These expand the product of an arbitrary Schubert class and a special Schubert class in the basis of Schubert classes. These special Schubert classes are indexed by a cycle which has either the form or the form , and are pulled back from a Grassmannian projection. Our formulas are in terms of certain labeled chains in the -Bruhat order on the symmetric group and are combinatorial in that they involve no cancellations. We also show that the multiplicities in the Pieri formula are naturally certain binomial coefficients.
9.
We prove a lower bound for the minimum distance of the linear code associated to a Schubert variety. Moreover for a Schubert variety of lines we compute the full distribution of weights. 相似文献
10.
Alexander Woo 《Advances in Mathematics》2006,207(1):205-220
11.
We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have recently been studied. The basic parameters such as the length, dimension and minimum distance of these codes are known only in special cases. An upper bound for the minimum distance is known and it is conjectured that this bound is achieved. We give explicit formulae for the length and dimension of arbitrary Schubert codes and prove the minimum distance conjecture in the affirmative for codes associated to Schubert divisors. 相似文献
12.
Vesselin Gasharov 《Compositio Mathematica》2001,126(1):47-56
We establish one direction of a conjecture by Lakshmibai and Sandhya which describes combinatorially the singular locus of a Schubert variety. We prove that the conjectured singular locus is contained in the singular locus. 相似文献
13.
14.
Christian Gutschwager 《Annals of Combinatorics》2010,14(3):339-353
In this paper we introduce a partial order on the set of skew characters of the symmetric group which we use to classify the
multiplicity-free skew characters. Furthermore, we give a short and easy proof that the Schubert calculus is equivalent to
that of skew characters in the following sense: If we decompose the product of two Schubert classes we get the same as if
we decompose a skew character and replace the irreducible characters by Schubert classes of the ‘inverse’ partitions (Theorem
4.3). 相似文献
15.
Daniel Cibotaru 《Mathematische Nachrichten》2020,293(3):449-474
We use incidence relations running in two directions in order to construct a Kempf–Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian. These constructions are alternatives to the celebrated Bott–Samelson resolutions. The second process led to the introduction of W-flag varieties, algebro-geometric objects that interpolate between the standard flag manifolds and products of Grassmannians, but which are singular in general. The surprising simple desingularization of a particular such type of variety produces an embedded resolution of the Schubert variety within the Grassmannian. 相似文献
16.
Jozsef Losonczy 《Annals of Combinatorics》2007,11(2):195-212
We introduce and study a class of “maximally clustered” elements for simply laced Coxeter groups. Such elements include as
a special case the freely braided elements of Green and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. We show that any reduced expression for a maximally clustered element is short-braid equivalent
to a “contracted” expression, which can be characterized in terms of certain subwords called “braid clusters”. We establish
some properties of contracted reduced expressions and apply these to the study of Schubert varieties in the simply laced setting.
Specifically, we give a smoothness criterion for Schubert varieties indexed by maximally clustered elements.
Received December 30, 2005 相似文献
17.
Aurélie Cortez 《Advances in Mathematics》2003,178(2):396-445
We determine explicitly the irreducible components of the singular locus of any Schubert variety for being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along each of them.The case of covexillary Schubert varieties was solved in an earlier work of the author [Ann. Inst. Fourier 51 (2) (2001) 375]. Here, we first exhibit some irreducible components of the singular locus of Xw, by describing the generic singularity along each of them. Let Σw be the union of these components. As mentioned above, the equality is known for covexillary varieties, and we base our proof of the general case on this result. More precisely, we study the exceptional locus of certain quasi-resolutions of a non-covexillary Schubert variety Xw, and we relate the intersection of these loci to Σw. Then, by induction on the dimension, we can establish the equality. 相似文献
18.
Andrzej Weber 《Selecta Mathematica, New Series》2016,22(3):1413-1454
We develop an equivariant version of the Hirzebruch class for singular varieties. When the group acting is a torus we apply localization theorem of Atiyah–Bott and Berline–Vergne. The localized Hirzebruch class is an invariant of a singularity germ. The singularities of toric varieties and Schubert varieties are of special interest. We prove certain positivity results for simplicial toric varieties. The positivity for Schubert varieties is illustrated by many examples, but it remains mysterious. 相似文献
19.
P. Magyar 《Commentarii Mathematici Helvetici》1998,73(4):603-636
Schubert polynomials generalize Schur polynomials, but it is not clear how to generalize several classical formulas: the
Weyl character formula, the Demazure character formula, and the generating series of semistandard tableaux. We produce these
missing formulas and obtain several surprising expressions for Schubert polynomials.?The above results arise naturally from
a new geometric model of Schubert polynomials in terms of Bott-Samelson varieties. Our analysis includes a new, explicit construction
for a Bott-Samelson variety Z as the closure of a B-orbit in a product of flag varieties. This construction works for an arbitrary reductive group G, and for G = GL(n) it realizes Z as the representations of a certain partially ordered set.?This poset unifies several well-known combinatorial structures:
generalized Young diagrams with their associated Schur modules; reduced decompositions of permutations; and the chamber sets
of Berenstein-Fomin-Zelevinsky, which are crucial in the combinatorics of canonical bases and matrix factorizations. On the
other hand, our embedding of Z gives an elementary construction of its coordinate ring, and allows us to specify a basis indexed by tableaux.
Received: November 27, 1997 相似文献
20.
We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic
subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the
classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the
product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer
coefficients, in terms of special Schubert class generators and relations. 相似文献