isaac90

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seen Jun 30 '13 at 16:08

Jun
29
awarded  Student
Jun
29
comment extension of torsion line bundles
Thanks again Sasha! A last question: why is any line bundle restricting to $\mathcal{O}_U$ in $U$ of the form $\mathcal{O}_X(D)$? What happens with multiplicities?
Jun
29
comment extension of torsion line bundles
I guess the more precise statement will be $\mathcal{O}_X(\sum a_i D_i)$ for some $a_i \geq 1$ and $D_i$ the irreducible components of $D$.
Jun
29
comment extension of torsion line bundles
Yes, $D$ need not be reduced. How do you it in that case?
Jun
29
comment extension of torsion line bundles
Hi Sasha. Thanks for the answer. Could you explain more in detail why there is a rational morphism $Y \to X$ and how do you do the "additional equivariant blowup $Y' \to Y$"? And why the resulting $L_X$ will satisfy $L_X^N=\mathcal{O}_X$? This will be very helpful for me.
Jun
29
awarded  Editor
Jun
29
revised extension of torsion line bundles
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Jun
29
asked extension of torsion line bundles