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I have a silly answer to your second question. Take a disjoint union of an elliptic curve with any other curve, and set L$L$ to be a nontrivial degree 0$0$ bundle on the elliptic curve and trivial on the other curve.
I have a silly answer to your second question. Take a disjoint union of an elliptic curve with any other curve, and set L to be a nontrivial degree 0 bundle on the elliptic curve and trivial on the other curve.
I have a silly answer to your second question. Take a disjoint union of an elliptic curve with any other curve, and set $L$ to be a nontrivial degree $0$ bundle on the elliptic curve and trivial on the other curve.
I have a silly answer to your second question. Take a disjoint union of an elliptic curve with any other curve, and set L to be a nontrivial degree 0 bundle on the elliptic curve and trivial on the other curve.
