On rank 2 vector bundles on fano manifolds

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It only takes a minute to sign up. As a first remark, the continuous and smooth classifications coincide, this is discussed e. More information can be found in. Theorem 3. The triviality here is in the topological or the smooth category. There is also a classical reference constructing rank 2 vector bundles on algebraic surfaces with prescribed Chern classes:.

This gives a more explicit construction which alternatively is known under the name Hartshorne-Serre correspondence. After fixing Chern classes and an additional invariant called the splitting type, the resulting moduli space of bundles has infinitely many irreducible components so that there are uncountably many algebraic structures on the trivial rank 2 bundle.

on rank 2 vector bundles on fano manifolds

As additional comment, We have Cartan-Serre theorem for construction of rank 2 vector bundles on projetive varieties. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 4 years, 2 months ago. Active 3 years, 2 months ago. Viewed 1k times. I see a theme forming. There is a section there discussing this question. Are you really interested in algebraic vector bundles? Active Oldest Votes. More information can be found in F.

Some remarks on Chern classes. There is also a classical reference constructing rank 2 vector bundles on algebraic surfaces with prescribed Chern classes: R. Vector bundles on algebraic surfaces. London Math.Download to read the full article text. Andreatta, M. AMS— Nagoya Math. Algebraic Geometry 7— Google Scholar. Beltrametti, M.

Cho, K. Higher dimensional birational geometry, Kyoto. Pure Math. Japan, Tokyo Fujita, T. Algebraic Geometry, Senday, North-Holland, Amsterdam In: Proceedings of the Conference in Alg. Geometry, Bayreuth Manuscripta Math. Kawamata, Y. Algebraic Geometry, Sendai, Maeda, H.

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Le Matematiche Catania 5073—82 Mori, S.As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

Fano bundles and splitting theorems on projective spaces and quadricsPacific J. Two theorems on elementary contractionsMath. DedicataTome 86 no. Projective manifolds whose tangent bundles are numerically effectiveMath. Conic bundles with big discriminant lociIzv. Nauk Ser. A remark on the topology of cyclic coverings of algebraic varietiesBoll. A 5Tome 18 no.

on rank 2 vector bundles on fano manifolds

AlgebraTome 31 no. Some special Cremona transformationsAmer. Notes Tome 6Abdus Salam Int. On the degrees of Fano four-folds of Picard number 1J. Reine Angew. Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1Ann. Fourier GrenobleTome 57 no. Birationality of the tangent map for minimal rational curvesAsian J.

Severi varieties and their varieties of reductionsJ. A Barth-type theorem for branched coverings of projective spaceMath. Boundedness of semistable sheaves of small ranksNagoya Math. Biregular classification of Fano 3 -folds and Fano manifolds of coindex 3Proc. On rank 2 vector bundles on Fano manifoldspreprint math. To appear in Kyoto J. Zbl preIn this work we deal with vector bundles of rank two on a Fano manifold X with second and fourth Betti numbers equal to one.

We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the vector bundle. As consequences, we obtain the complete list of P 1 -bundles over X that have a second P 1 -bundle structure, classify all the uniform rank two vector bundles on this class of Fano manifolds, and show the stability of indecomposable Fano bundles with one exception on P 2.

Source Kyoto J. Zentralblatt MATH identifier Kyoto J. More by Luis E. Abstract Article info and citation First page References Abstract In this work we deal with vector bundles of rank two on a Fano manifold X with second and fourth Betti numbers equal to one.

Article information Source Kyoto J.

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Addeddate External-identifier urn:arXiv There are no reviews yet. Be the first one to write a review. Additional Collections.In these cases, you need to analyze the data using Analysis of Variance, which can be considered to be a generalization of the t-test. However, when the design is more complex, ANOVA offers numerous advantages that t-tests cannot provide (even if you run a series of t- tests comparing various cells of the design).

To index Within-group Variation. As explained in Elementary Concepts, the size of a relation between two variables, such as the one measured by a difference in means between two groups, depends to a large extent on the differentiation of values within the group. Depending on how differentiated the values are in each group, a given "raw difference" in group means will indicate either a stronger or weaker relationship between the independent (grouping) and dependent variable.

However, if the same difference of 2 was obtained from very differentiated scores (e. That is to say, reduction of the within-group variation increases the sensitivity of our test. The t-test for dependent samples helps us to take advantage of one specific type of design in which an important source of within-group variation (or so-called, error) can be easily identified and excluded from the analysis.

Specifically, if two groups of observations (that are to be compared) are based on the same sample of subjects who were tested twice (e. However, if the same sample was tested twice, then we can easily identify (or "subtract") this variation.

Specifically, instead of treating each group separately, and analyzing raw scores, we can look only at the differences between the two measures (e. By subtracting the first score from the second for each subject and then analyzing only those "pure (paired) differences," we will exclude the entire part of the variation in our data set that results from unequal base levels of individual subjects.

This is precisely what is being done in the t-test for dependent samples, and, as compared to the t-test for independent samples, it always produces "better" results (i. If these assumptions are clearly not met, then one of the nonparametric alternative tests should be used. Technically, we can apply the t-test for dependent samples to any two variables in our data set. However, applying this test will make very little sense if the values of the two variables in the data set are not logically and methodologically comparable.

Following, is an example of a data set that can be analyzed using the t-test for dependent samples. WCC before WCC after case 1 case 2 case 3 case 4 case 5. However, the t-test for dependent samples analysis is performed only on the paired differences"ignoring" the raw scores and their potential differentiation.

Thus, the size of this particular difference of 1 will be compared not to the differentiation of raw scores but to the differentiation of the individual difference scores, which is relatively small: 0.

Compared to that variability, the difference of 1 is extremely large and can yield a highly significant t value.

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If there are more than two "correlated samples" (e. The repeated measures ANOVA can be considered a generalization of the t-test for dependent samples and it offers various features that increase the overall sensitivity of the analysis.

The breakdowns analysis calculates descriptive statistics and correlations for dependent variables in each of a number of groups defined by one or more grouping (independent) variables. In the following example data set (spreadsheet), the dependent variable WCC (White Cell Count) can be broken down by 2 independent variables: Gender (values: males and females), and Height (values: tall and short).Yes No Share on Facebook Share on Twitter Stop in for my second routine oil change vehicle maintenance check.

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on rank 2 vector bundles on fano manifolds

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