2 problems

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Lins Neto's rational first-integral conjecture for polynomial systems
Let $P(x,y)$ and $Q(x,y)$ define a polynomial system … of degree $d$ , and suppose the system has an invariant algebraic curve whose degree is sufficiently high, with the bound depe…
Conjecturerefutedinvariant-curves polynomial-differential-systems rational-first-integralsarXiv posted 2 days ago
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The symmetry-component conjecture for polynomial differential systems
Symmetry-component conjecture. For any polynomial system of the form $$, $mathbf V(I{sym})$ is a component of the center variety.
Conjectureopenalgebraic-geometry center-varieties polynomial-differential-systemsarXiv posted 2 days ago

Lins Neto's rational first-integral conjecture for polynomial systems