The Nagata conjecture for plane curves predicts the strict degree-multiplicity inequality
for a nonzero effective complex projective plane curve of degree at very general distinct points with prescribed nonnegativeinteger multiplicities no larger than the actual multiplicities. Repeated or reducible
components and unequal multiplicities are allowed. Very general means outside a countable
union of proper Zariski-closed subsets of the ordered configuration space.
Ciliberto, C.; Harbourne, B.; Miranda, R.; and Roé, J. "Variations on Nagata's Conjecture." In A Celebration of Algebraic
Geometry (Ed. B. Hassett, J. McKernan, J. Starr, and R. Vakil).
Providence, RI: Amer. Math. Soc., pp. 185-203, 2013. https://www.math.colostate.edu/~miranda/preprints/CHMR130122clayStyle.pdf.
at 
very general distinct points with prescribed nonnegative integer multiplicities 
no larger than the actual multiplicities. Repeated or reducible
components and unequal multiplicities are allowed. Very general means outside a countable
union of proper Zariski-closed subsets of the ordered configuration space.
