A method for producing a self-supporting integral-asymmetric hollow fiber polymer membrane with an isoporous outer skin in which the pores of the separation-active outer skin have a maximum pore diameter to minimum pore diameter ratio of less than 3, with a porous inner skin and foam-like inner structure, in a dry/wet spinning method, comprising the following method steps: - production of a polymer solution with at least one solvent in which at least one amphiphilic block copolymer is dissolved with at least two different polymer blocks, wherein the block copolymers and the polymer blocks have a low polydispersity of less than 1.5, and the polymer lengths of the at least two polymer blocks of the amphiphilic block copolymer relative to each other are selected so that a self-organization in the solvent leads to the formation of a spherical, cylindrical or co-continuous, in particular gyroidal, micellar structure or microphase structure in the solvent with a length ratio between approximately 2:1 and approximately 10:1, - pressing the polymer solution with an overpressure of 0.01 to 0.5 bar through a spinning nozzle designed as a hollow core nozzle or multiple hollow core nozzle to form a hollow fiber, in the middle of which a liquid column is spun that consists of a precipitant with reduced precipitation activity, wherein the liquid column consists of a mixture of at least one precipitant for the at least one block copolymer and at least one solvent that can be mixed with the precipitant for the at least one block copolymer, wherein in particular at least one additional pore former, in particular polyethylene glycol, is present in the liquid column, - after falling a fall distance with a length of 1 cm to 100 cm in an atmosphere, immersion of the spun hollow fiber in a precipitation bath to form the hollow fiber polymer membrane. - production of a polymer solution with at least one solvent in which at least one amphiphilic block copolymer is dissolved with at least two different polymer blocks, wherein the block copolymers and the polymer blocks have a low polydispersity of less than 1.5, and the polymer lengths of the at least two polymer blocks of the amphiphilic block copolymer relative to each other are selected so that a self-organization in the solvent leads to the formation of a spherical, cylindrical or co-continuous, in particular gyroidal, micellar structure or microphase structure in the solvent with a length ratio between approximately 2:1 and approximately 10:1, - pressing the polymer solution with an overpressure of 0.01 to 0.5 bar through a spinning nozzle designed as a hollow core nozzle or multiple hollow core nozzle to form a hollow fiber, in the middle of which a liquid column is spun that consists of a precipitant with reduced precipitation activity, wherein the liquid column consists of a mixture of at least one precipitant for the at least one block copolymer and at least one solvent that can be mixed with the precipitant for the at least one block copolymer, wherein in particular at least one additional pore former, in particular polyethylene glycol, is present in the liquid column, - after falling a fall distance with a length of 1 cm to 100 cm in an atmosphere, immersion of the spun hollow fiber in a precipitation bath to form the hollow fiber polymer membrane.