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pro vyhledávání: '"Casnati, Gianfranco"'
We study varieties $X \subset P^r$ such that is $N_X^*(k)$ is an Ulrich vector bundle for some integer $k$. We first prove that such an $X$ must be a curve. Then we give several examples of curves with $N_X^*(k)$ an Ulrich vector bundle.
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Comment
Externí odkaz:
http://arxiv.org/abs/2306.00113
Autor:
Casnati, Gianfranco
In this very short note we give an elementary characteristic free proof of the result claimed in the title (see Theorem 1.2 for a more precise formulation), generalizing a recent result proved for Ulrich bundles over the complex field by V. Benedetti
Externí odkaz:
http://arxiv.org/abs/2303.04064
Let $X$ be a Fano threefold with index $i_X$ and fundamental line bundle $\mathcal O_X(h)$. We classify $\mu$-semistable rank two bundles $\mathcal E$ on $X$ with $c_1(\mathcal E)=0$, $h^0(\mathcal E) \ne 0$ and $h^1(\mathcal E(-\lceil\frac{i_X}{2}\r
Externí odkaz:
http://arxiv.org/abs/2212.04158
Let $X\subseteq{\mathbb P}^{n+1}$ be an integral hypersurface of degree $d$. We show that each locally Cohen-Macaulay instanton sheaf $\mathcal E$ on $X$ with respect to $\mathcal O_X\otimes\mathcal O_{\mathbb P^{n+1}}(1)$ in the sense of Definition
Externí odkaz:
http://arxiv.org/abs/2210.03408
A $h$-instanton sheaf on a closed subscheme $X$ of some projective space endowed with an ample and globally generated line bundle $\mathcal{O}_X(h)$ is a coherent sheaf whose cohomology table has a certain prescribed shape. In this paper we deal with
Externí odkaz:
http://arxiv.org/abs/2205.04767
We define non-ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) instanton bundles. We determine a lower bound for the quantum number of a non-ordinary instanton bundle, i.e. the degree of its second Chern class, sho
Externí odkaz:
http://arxiv.org/abs/2105.00632
In this paper we deal with a particular class of rank two vector bundles (\emph{instanton} bundles) on the Fano threefold of index one $F:=\mathbb{F}_1 \times \mathbb{P}^1$. We show that every instanton bundle on $F$ can be described as the cohomolog
Externí odkaz:
http://arxiv.org/abs/2103.04411
Autor:
Casnati, Gianfranco, Genc, Ozhan
We deal with instanton bundles on the product ${\mathbb P}^1\times{\mathbb P}^2$ and the blow up of ${\mathbb P}^3$ along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth poi
Externí odkaz:
http://arxiv.org/abs/2004.03415
We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on $\mathbb P^3$ and on Fano threefold with cyclic Picard group. Then we deal with the case of the blow up of
Externí odkaz:
http://arxiv.org/abs/1909.10281
Autor:
Casnati, Gianfranco
We give examples of surfaces which are Ulrich-wild, i.e. that support families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.
Comment: 15 pages. Several typos have been fixed. The proof of Th
Comment: 15 pages. Several typos have been fixed. The proof of Th
Externí odkaz:
http://arxiv.org/abs/1810.00755