  We explore the correspondence between Yang-Mills instantons and algebraic
curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4
dimensional Yang-Mills-Higgs theory, and it is identified in string theory with
the cross-section of supertubes connecting parallel D4-branes. To present
evidence for the identification, we show that with total charges fixed, the
supertube angular momentum computed from the Higgs zero locus is maximized when
the locus is circular, which has been proven for the cross-section of the
supertubes. This leads to a consistent dictionary between the charges in two
pictures. We also consider a T-dual version of the story, identifying the
profiles of the wavy instanton strings with those of the supercurves/D-helices.
Based on this observation, we then argue a novel correspondence between ADHM
data of instantons and algebraic curves defining the locus. The degree of the
curve is related to the instanton number, and splitting property of the curve
is physically manifested by well-separated instantons.
