共查询到20条相似文献,搜索用时 485 毫秒
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Boris Pasquier 《Mathematische Annalen》2009,344(4):963-987
We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any
such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbit varieties with Picard number 1 that satisfy
this latter property. 相似文献
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Susan Cooper Brian Harbourne Zach Teitler 《Journal of Pure and Applied Algebra》2011,215(9):2165-2179
We study Hilbert functions of certain non-reduced schemes A supported at finite sets of points in , in particular, fat point schemes. We give combinatorially defined upper and lower bounds for the Hilbert function of A using nothing more than the multiplicities of the points and information about which subsets of the points are linearly dependent. When N=2, we give these bounds explicitly and we give a sufficient criterion for the upper and lower bounds to be equal. When this criterion is satisfied, we give both a simple formula for the Hilbert function and combinatorially defined upper and lower bounds on the graded Betti numbers for the ideal IA defining A, generalizing results of Geramita et al. (2006) [16]. We obtain the exact Hilbert functions and graded Betti numbers for many families of examples, interesting combinatorially, geometrically, and algebraically. Our method works in any characteristic. 相似文献
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Christian Liedtke 《Mathematische Zeitschrift》2008,259(4):775-797
We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces
of general type with non-trivial global vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as surfaces
with inseparable canonical maps. In particular, we show that some previously known pathologies are not sporadic but exist
in abundance. 相似文献
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Marta Pérez Rodríguez 《Journal of Pure and Applied Algebra》2008,212(11):2381-2388
We provide the main results of a deformation theory of smooth formal schemes as defined in [L. Alonso Tarrío, A. Jeremías López, M. Pérez Rodríguez, Infinitesimal lifting and Jacobi criterion for smoothness on formal schemes, Comm. Algebra 35 (2007) 1341-1367]. Smoothness is defined by the local existence of infinitesimal liftings. Our first result is the existence of an obstruction in a certain Ext1 group whose vanishing guarantees the existence of global liftings of morphisms. Next, given a smooth morphism f0:X0→Y0 of noetherian formal schemes and a closed immersion Y0?Y given by a square zero ideal I, we prove that the set of isomorphism classes of smooth formal schemes lifting X0 over Y is classified by and that there exists an element in which vanishes if and only if there exists a smooth formal scheme lifting X0 over Y. 相似文献
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Joseph W. Cutrone Nicholas A. Marshburn 《Central European Journal of Mathematics》2013,11(9):1552-1576
In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven. 相似文献
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Federico Binda 《Journal of Pure and Applied Algebra》2018,222(1):61-74
In this note, we show that given a smooth affine variety X over an algebraically closed field k and an effective (possibly non-reduced) Cartier divisor on it, the Chow group of zero cycles with modulus is torsion free, except possibly for p-torsion if the characteristic of k is . This generalizes to the relative setting classical results of Rojtman (for X smooth) and of Levine (for X singular). 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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Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2011,215(2):168-184
Let X be a smooth complex projective variety of dimension 3 and let L be an ample line bundle on X. In this paper, we provide a lower bound for h0(m(KX+L)) under the assumption that κ(KX+L)≥0. In particular, we get the following: (1) if 0≤κ(KX+L)≤2, then h0(KX+L)>0 holds. (2) If κ(KX+L)=3, then h0(2(KX+L))≥3 holds. Moreover we get a classification of (X,L) with κ(KX+L)=3 and h0(2(KX+L))=3 or 4. 相似文献
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Anita Buckley 《Linear algebra and its applications》2010,433(4):758-780
Let C be a smooth curve in P2 given by an equation F=0 of degree d. In this paper we consider elementary transformations of linear pfaffian representations of C. Elementary transformations can be interpreted as actions on a rank 2 vector bundle on C with canonical determinant and no sections, which corresponds to the cokernel of a pfaffian representation. Every two pfaffian representations of C can be bridged by a finite sequence of elementary transformations. Pfaffian representations and elementary transformations are constructed explicitly. For a smooth quartic, applications to Aronhold bundles and theta characteristics are given. 相似文献
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Toru Tsukioka 《manuscripta mathematica》2010,132(1-2):247-255
The Picard number of a Fano manifold X obtained by blowing up a curve in a smooth projective variety is known to be at most 5, in any dimension greater than or equal to 4. In this note, we show that the Picard number attains to the maximal if and only if X is the blow-up of the projective space whose center consists of two points, the strict transform of the line joining them and a linear subspace or a hyperquadric of codimension 2. This result is obtained as a consequence of a classification of special types of Fano manifolds. 相似文献
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Let k be a field that is not algebraically closed, and let A be a k-algebra, whose each maximal ideal has residue field k. We prove that each element of the Picard group of A is of finite order and give an optimal upper bound for its order. 相似文献
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Atoshi Chowdhury 《Journal of Pure and Applied Algebra》2019,223(10):4283-4301
Over a family of varieties with singular special fiber, the relative Picard functor (i.e. the moduli space of line bundles) may fail to be compact. We propose a stability condition for line bundles on reducible varieties that is aimed at compactifying it. This stability condition generalizes the notion of ‘balanced multidegree’ used by Caporaso in compactifying the relative Picard functor over families of curves. Unlike the latter, it is defined ‘asymptotically’; an important theme of this paper is that although line bundles on higher-dimensional varieties are more complicated than those on curves, their behavior in terms of stability asymptotically approaches that of line bundles on curves.Using this definition of stability, we prove that over a one-parameter family of varieties having smooth total space, any line bundle on the generic fiber can be extended to a unique semistable line bundle on the (possibly reducible) special fiber, provided the special fiber is not too complicated in a combinatorial sense. 相似文献
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Ivan PaninSerge Yagunov 《Journal of Pure and Applied Algebra》2002,172(1):49-77
In the following paper we introduce the notion of orientable functor (orientable cohomology theory) on the category of projective smooth schemes and define a family of transfer maps. Applying this technique, we prove that with finite coefficients orientable cohomology of a projective variety is invariant with respect to the base-change given by an extension of algebraically closed fields. This statement generalizes the classical result of Suslin, concerning algebraic K-theory of algebraically closed fields. Besides K-theory, we treat such examples of orientable functors as etale cohomology, motivic cohomology, algebraic cobordism. We also demonstrate a method to endow algebraic cobordism with multiplicative structure and Chern classes. 相似文献
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Gereon Quick 《Advances in Mathematics》2007,214(2):730-760
We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an étale topological realization of the stable A1-homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero.On the other hand we get a natural setting for étale cohomology theories. In particular, we define and discuss an étale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from étale cohomology. Finally, we construct maps from algebraic to étale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a Bott element. 相似文献
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Riccardo Ghiloni 《Topology and its Applications》2007,154(17):3090-3094
Let Y be a compact nonsingular real algebraic set whose homology classes (over Z/2) are represented by Zariski closed subsets. It is well known that every smooth map from a compact smooth manifold to Y is unoriented bordant to a regular map. In this paper, we show how to construct smooth maps from compact nonsingular real algebraic sets to Y not homotopic to any regular map starting from a nonzero homology class of Y of positive degree. We use these maps to obtain obstructions to the existence of local algebraic tubular neighborhoods of algebraic submanifolds of Rn and to study some algebro-homological properties of rational real algebraic manifolds. 相似文献
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Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2007,211(3):609-621
Let (X,L) be a polarized manifold of dimension n defined over the field of complex numbers. In this paper, we treat the case where n=3 and 4. First we study the case of n=3 and we give an explicit lower bound for h0(KX+L) if κ(X)≥0. Moreover, we show the following: if κ(KX+L)≥0, then h0(KX+L)>0 unless κ(X)=−∞ and h1(OX)=0. This gives us a partial answer of Effective Non-vanishing Conjecture for polarized 3-folds. Next for n=4 we investigate the dimension of H0(KX+mL) for m≥2. If n=4 and κ(X)≥0, then a lower bound for h0(KX+mL) is obtained. We also consider a conjecture of Beltrametti-Sommese for 4-folds and we can prove that this conjecture is true unless κ(X)=−∞ and h1(OX)=0. Furthermore we prove the following: if (X,L) is a polarized 4-fold with κ(X)≥0 and h1(OX)>0, then h0(KX+L)>0. 相似文献
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