What question did this study set out to answer?

The study aims to classify algebraic curves that are invariant under infinite subgroups of projective transformations.

Exceptional algebraic curves for infinite subgroups of PGL( n +1,ℂ)

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Technical study classifies irreducible curves invariant under infinite projective transformations, highlighting implications for group actions.

The study aims to classify algebraic curves that are invariant under infinite subgroups of projective transformations.
Classified irreducible non-degenerate curves preserved by projective transformations of infinite order.
Analyzed induced actions on the projective span of curves for cases that are not virtually trivial.
Derived consequences for group-level actions using the Zariski closure.
If the induced action is not virtually trivial, the curve is equivalent to a rational monomial curve.
Every irreducible component with non-trivial induced action is a rational monomial curve.
Discrete nonvirtually cyclic actions limit essential invariant curves to projective lines or rational normal curves.

Cano et al. (2026) studied this question.

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Technical study classifies irreducible curves invariant under infinite projective transformations, highlighting implications for group actions.