4 problems

Strong Fujita freeness conjecture. The linear system

Let $S$ be a smooth projective surface and let $H_i$ be a very ample divisor as in the source. Fujita's conjecture. The divisor … is very ample. Consequently, under the hypotheses…

Helmke's numerical Fujita freeness conjecture. Under these conditions, the adjoint divisor

The pointwise base-point-freeness conjecture. The adjoint line bundle $K_Y+L$ is base point free at $y$. The source presents this as a known generalization of Fujita's base point f…