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Suppose $X$ is a complex manifold, we have the map $H^0(X,K_X/O_X)\to H^1(X,O_X^*)$$H^0(X,K_X^*/O_X^*)\to H^1(X,O_X^*)$, is the canonical line bundle $\wedge^n{\Omega}$ always in the image of the map?
Suppose $X$ is a complex manifold, we have the map $H^0(X,K_X/O_X)\to H^1(X,O_X^*)$, is the canonical line bundle $\wedge^n{\Omega}$ always in the image of the map?
Suppose $X$ is a complex manifold, we have the map $H^0(X,K_X^*/O_X^*)\to H^1(X,O_X^*)$, is the canonical line bundle $\wedge^n{\Omega}$ always in the image of the map?
Must a canonical line bundle be associated to a cartier divisor?
Suppose $X$ is a complex manifold, we have the map $H^0(X,K_X/O_X)\to H^1(X,O_X^*)$, is the canonical line bundle $\wedge^n{\Omega}$ always in the image of the map?
