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Ulrich bundles on smooth projective varieties of minimal degree
TLDR
In this paper, the stability of the sheaves of relative differentials on rational scrolls has been shown for smooth projective varieties of minimal degree, and it has also been shown that the stable sheaves can be computed on rational scroll.Abstract:
We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree In the process, we prove the stability of the sheaves of relative differentials on rational scrollsread more
Citations
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On the positivity of the first Chern class of an Ulrich vector bundle
TL;DR: In this paper, the positivity of the first Chern class of rank r Ulrich vector bundles on a smooth n-dimensional variety was studied, and it was shown that the rank r uulrich vector bundle E is very positive on every subvariety not contained in the union of lines in X. In particular, if X is not covered by lines, then E is big and
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Characterization of Ulrich bundles on Hirzebruch surfaces
TL;DR: In this paper, the authors characterized the existence of stable Ulrich bundles of any rank on polarized rational ruled surfaces and showed that every Ulrich bundle admits a resolution in terms of line bundles, given an injective map between suitable totally decomposed vector bundles.
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H-instanton bundles on three-dimensional polarized projective varieties
TL;DR: In this paper, the instanton bundle on any projective variety of dimension three polarized by a very ample divisor was introduced and a monadic description of instanton bundles on three-dimensional rational normal scrolls was given.
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Instanton bundles on the Segre threefold with Picard number three
TL;DR: In this article, the authors studied instanton bundles on the lines for any possible $c_2(E) and showed that the Gieseker case is semistable on the line.
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Ulrich and aCM bundles from invariant theory
TL;DR: In this paper, it was shown that a general cubic hypersurface of dimension seven admits an indecomposable Ulrich vector bundle of rank nine, and that general cubic fourfold admits an unsplit CM vector bundle with rank six.
References
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Book
Cohen-Macaulay modules over Cohen-Macaulay rings
TL;DR: CM(R)は有�’�生成加群の圏mod (R)の resolventな充満部分圏である。
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Projective bundles, monoidal transformations, and derived categories of coherent sheaves
TL;DR: In this paper, the authors derived categories of coherent sheaves on varieties that are obtained by projectivization of vector bundles and by monoidal transformations conditions for the existence of complete exceptional sets in such categories are derived; they give new examples of varieties on which exceptional sets exist.
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Cohen-Macaulay modules on hypersurface singularities II
TL;DR: In this paper, the authors present a generalization of matrix factorizations to matrix factorization on A~ and D. The results show that the matrix factorisation on D can be expressed as a matrix decomposition of a periodic complex.