Global sections of square root line bundle The Next CEO of Stack OverflowGenerators of the ring of sections of a line bundleSimple example of an ample line bundle that is not very ampleExample for very ample line bundle numerically equivalent to a not very ample line bundleLine Bundle of deg 2g-1 and generated by global sectionsGlobal sections when we tensor by a degree zero line bundleGlobal sections of tensor powers of a line bundleAmple, Very ample line bundles on projective spaceObstructions for a root of a given line bundle on a curve over arbitrary base field to existDimension of global sections of an ample line bundle lower boundDoes the line bundle have global sections?
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Global sections of square root line bundle
The Next CEO of Stack OverflowGenerators of the ring of sections of a line bundleSimple example of an ample line bundle that is not very ampleExample for very ample line bundle numerically equivalent to a not very ample line bundleLine Bundle of deg 2g-1 and generated by global sectionsGlobal sections when we tensor by a degree zero line bundleGlobal sections of tensor powers of a line bundleAmple, Very ample line bundles on projective spaceObstructions for a root of a given line bundle on a curve over arbitrary base field to existDimension of global sections of an ample line bundle lower boundDoes the line bundle have global sections?
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
add a comment |
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
add a comment |
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
edited Mar 20 at 13:27
Stefano
2,223931
edited Mar 20 at 13:27
Stefano
2,223931
edited Mar 20 at 13:27
Stefano
2,223931
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
1,313720
add a comment |
add a comment |
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