Positive genus for a scheme that doesn't define curve

[Georgi Guninski]

#Author Georgi Guninski

K.<x,y,z,t>=QQ[]
t1=x^2*z^2 + y*t;
t2= y*z^2 + x^2*t;
C=Curve([x^4-y^2-19,z^4-t^2-23,t1^2-t2^2-19*23]);
C.genus()
#93 #Wrong

C.irreducible_components()
[
Closed subscheme of Affine Space of dimension 4 over Rational Field defined by:
z^4 - t^2 - 23,
x^4 - y^2 - 19
]

Magma raises error when trying to construct Curve()

When I work over GF(113) instead of QQ, I get error:

RuntimeError: error in Singular function call 'genus':
This is not a curve
leaving normal.lib::genus (0)

[Nils Bruin]

The irreducible_components gives an answer that is consistent with magma: C is a complete intersection of two hypersurfaces in A4 and hence of dimension 2 itself. Looks like "Curve" over QQ doesn't check dimension or delegates to a routine that doesn't check properly.

[Kwankyu Lee]

 Looks like "Curve" over QQ doesn't check dimension or delegates to a routine that doesn't check properly.

It is the latter case. There is a subtle bug in curve constructors. 

[Kwankyu Lee]

Fixed in https://github.com/sagemath/sage/pull/38414