Let $(F,\cO_F(1))$ be a smooth polarized projective variety of dimension $n$. In the present paper we prove some easy results on aCM bundles of rank $2$ on $F$, i.e. locally free sheaves $\cE$ of rank $2$ on $F$ such that $h^i\big(F,\cE(t)\big)=0$, for $i=1,\dots,n-1$ and $t\in\bZ$. We obtain some results in the case of a very ample polarization when $n\ge5$. We apply these results in order to deal with bundles on non--degenerate complete intersection with degree up to $9$. A complete description is given for the complete intersections of two quadrics when $n\ge4$.

On rank two aCM bundles / Casnati, Gianfranco. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 45:10(2017), pp. 4139-4157. [10.1080/00927872.2016.1222397]

On rank two aCM bundles

CASNATI, GIANFRANCO
2017

Abstract

Let $(F,\cO_F(1))$ be a smooth polarized projective variety of dimension $n$. In the present paper we prove some easy results on aCM bundles of rank $2$ on $F$, i.e. locally free sheaves $\cE$ of rank $2$ on $F$ such that $h^i\big(F,\cE(t)\big)=0$, for $i=1,\dots,n-1$ and $t\in\bZ$. We obtain some results in the case of a very ample polarization when $n\ge5$. We apply these results in order to deal with bundles on non--degenerate complete intersection with degree up to $9$. A complete description is given for the complete intersections of two quadrics when $n\ge4$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2669805
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