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user39380

Examples for curve not 1-connected but $h^0(C, O_C)=1$

Suppose $X$ is a surface, are there examples for curves on X which not 1-connected, but $h^0(C)=1$$h^0(C,O_C)=1$? (Here a curve is an effective divisor, not necessarily reduced or irreducible) (1-connectedness means when it splits into two effective divisors, the two parts have intesection number greater than or equal to 1)

Another question is I am not sure if the dimension of cohomology and 1-connectedness is preserved by linear equivalence ?

Examples for curve not 1-connected but $h^0(C)=1$

Suppose $X$ is a surface, are there examples for curves on X which not 1-connected, but $h^0(C)=1$? (Here a curve is an effective divisor, not necessarily reduced or irreducible) (1-connectedness means when it splits into two effective divisors, the two parts have intesection number greater than or equal to 1)

Examples for curve not 1-connected but $h^0(C, O_C)=1$

Suppose $X$ is a surface, are there examples for curves on X which not 1-connected, but $h^0(C,O_C)=1$? (Here a curve is an effective divisor, not necessarily reduced or irreducible) (1-connectedness means when it splits into two effective divisors, the two parts have intesection number greater than or equal to 1)

Another question is I am not sure if the dimension of cohomology and 1-connectedness is preserved by linear equivalence ?

Source Link
user39380
user39380

Examples for curve not 1-connected but $h^0(C)=1$

Suppose $X$ is a surface, are there examples for curves on X which not 1-connected, but $h^0(C)=1$? (Here a curve is an effective divisor, not necessarily reduced or irreducible) (1-connectedness means when it splits into two effective divisors, the two parts have intesection number greater than or equal to 1)