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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 |