It is known there is an explicit algebraic variety in $mathbb Z[x_1,dots,x_t]$ a bounded $t>2$ whose integral zero-set is non-empty is undecidable. If the variety has genus $0$ is there anything known about decidability? If the variety has genus $0$ and $t=2$ is there anything known about decidability?

Genus $0$ algebraic curves integral points decidable?

MathOverflow Asked by 1.. on November 14, 2020

It is known there is an explicit algebraic variety in $mathbb Z[x_1,dots,x_t]$ a bounded $t>2$ whose integral zero-set is non-empty is undecidable.

If the variety has genus $0$ is there anything known about decidability?
If the variety has genus $0$ and $t=2$ is there anything known about decidability?

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