Every ternary quintic is a sum of ten fifth powers

摘要

To our knowledge at the time of writing, the maximum Waring rank for the set of all ternary forms of degree d (with coefficients in an algebraically closed field of characteristic zero) is known only for d <= 4, and the best upper bound that is known for d = 5 is 12. In this work, we lower the upper bound to 10 (and there are evidences that it is likely sharp).