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edited Apr 13, 2017 at 12:19

Crossposted from MSE MSE.

I am interested what is the type of the surfaces over the rationals $$ x^5 - y^5 + z^2 + x=0$$

and

$$ x^5 - y^5 + z^2 + x+1=0$$

Magma's KodairaEnriquesType(S : CheckADE:=true); fails to compute it.

According to Magma they are not rational.

Partial answers (e.g. it is not $X$) or approaches how to compute with a CAS are welcome.

Crossposted from MSE.

I am interested what is the type of the surfaces over the rationals $$ x^5 - y^5 + z^2 + x=0$$

and

$$ x^5 - y^5 + z^2 + x+1=0$$

Magma's KodairaEnriquesType(S : CheckADE:=true); fails to compute it.

According to Magma they are not rational.

Partial answers (e.g. it is not $X$) or approaches how to compute with a CAS are welcome.

Crossposted from MSE.

I am interested what is the type of the surfaces over the rationals $$ x^5 - y^5 + z^2 + x=0$$

and

$$ x^5 - y^5 + z^2 + x+1=0$$

Magma's KodairaEnriquesType(S : CheckADE:=true); fails to compute it.

According to Magma they are not rational.

Partial answers (e.g. it is not $X$) or approaches how to compute with a CAS are welcome.

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asked Aug 19, 2015 at 8:19

What is the type of the surfaces $x^5 - y^5 + z^2 + x=0$ and $x^5 - y^5 + z^2 + x+1=0$?

Crossposted from MSE.

I am interested what is the type of the surfaces over the rationals $$ x^5 - y^5 + z^2 + x=0$$

and

$$ x^5 - y^5 + z^2 + x+1=0$$

Magma's KodairaEnriquesType(S : CheckADE:=true); fails to compute it.

According to Magma they are not rational.

Partial answers (e.g. it is not $X$) or approaches how to compute with a CAS are welcome.