Abstract
Let \(F\subseteq {\mathbb {P}^{3}}\) be a smooth quartic surface and let \({\mathcal {O}}_F(h):={\mathcal {O}}_{{\mathbb {P}^{3}}}(1)\otimes {\mathcal {O}}_F\). In the present paper we classify locally free sheaves \({\mathcal {E}}\) of rank 2 on F such that \(c_1({\mathcal {E}})={\mathcal {O}}_F(2h), c_2({\mathcal {E}})=8\) and \(h^1\big (F,{\mathcal {E}}(th)\big )=0\) for \(t\in \mathbb {Z}\). We also deal with their stability.
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This paper is dedicated to Ph. Ellia on the occasion of his 60th birthday.
The authors are members of the GNSAGA group of INdAM and are supported by the framework of PRIN 2010/11 ‘Geometria delle varietà algebriche’, cofinanced by MIUR.
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Casnati, G., Notari, R. Examples of rank two aCM bundles on smooth quartic surfaces in \({\mathbb {P}^{3}}\) . Rend. Circ. Mat. Palermo, II. Ser 66, 19–41 (2017). https://doi.org/10.1007/s12215-016-0272-8
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DOI: https://doi.org/10.1007/s12215-016-0272-8