Resumen de Linear Estimate for the Number of Zeros of Abelian Integrals

Dmitry Novikov, Sergey Malev

• We prove a linear in deg ω upper bound on the number of real zeros of the Abelian integral I(t) = δ(t) ω, where δ(t) ⊂ R2 is the real oval x2 y(1 − x − y) = t and ω is a one-form with polynomial coefficients.