A proof of Coleman's conjecture

Almost thirty years ago Coleman made a conjecture that for any convex lattice polygon with vv vertices, gg (g⩾1g⩾1) interior lattice points and bb boundary lattice points we have b⩽2g-v+10b⩽2g-v+10. In this note we give a proof of the conjecture. We also aim to describe all convex lattice polygons for which the bound b=2g-v+10b=2g-v+10 is attained.