The following Bertini theorem is proved: if F is a reflexive sheaf of rank 2 over a smooth projective variety X where F is generated by global sections then the general section of F(n), $n\ge 1$, defines an integral subvariety of codimension 2 in X. \par In the case $X={\bbfP}\sb 3$, some properties of the function h(p) characterize locally-free sheaves on ${\bbfP}\sb 3$. Here $h(p)=h\sp 2F(p)-h\sp 1(F(p)\otimes \omega\sb{{\bbfP}\sb 3}(3))$. In fact, F is a vector bundle over ${\bbfP}\sb 3$ if and only if $h(p)=0$ for $p=(c\sb 1- 4)/2$.
Teoremi di Bertini, fasci riflessivi e curve sottocanoniche
ROGGERO, Margherita
1988-01-01
Abstract
The following Bertini theorem is proved: if F is a reflexive sheaf of rank 2 over a smooth projective variety X where F is generated by global sections then the general section of F(n), $n\ge 1$, defines an integral subvariety of codimension 2 in X. \par In the case $X={\bbfP}\sb 3$, some properties of the function h(p) characterize locally-free sheaves on ${\bbfP}\sb 3$. Here $h(p)=h\sp 2F(p)-h\sp 1(F(p)\otimes \omega\sb{{\bbfP}\sb 3}(3))$. In fact, F is a vector bundle over ${\bbfP}\sb 3$ if and only if $h(p)=0$ for $p=(c\sb 1- 4)/2$.
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