Fixes for reviewer comments

src/sage/rings/function_field/function_field_polymod.py

@@ -41,9 +41,6 @@
 from .function_field import FunctionField
 from .function_field_rational import RationalFunctionField
 
-_FunctionFields = FunctionFields()
-_NumberFields = NumberFields()
-
 
 class FunctionField_polymod(FunctionField):
     """
@@ -164,7 +161,7 @@ def __init__(self, polynomial, names, category=None):
         self._polynomial = polynomial
 
         FunctionField.__init__(self, base_field, names=names,
-                               category=_FunctionFields.or_subcategory(category))
+                               category=FunctionFields().or_subcategory(category))
 
         from .place_polymod import FunctionFieldPlace_polymod
         self._place_class = FunctionFieldPlace_polymod
@@ -1861,7 +1858,7 @@ def genus(self):
         The genus is computed by the Hurwitz genus formula.
         """
         k, _ = self.exact_constant_field()
-        if k in _NumberFields:
+        if k in NumberFields():
             k_degree = k.relative_degree()
         else:
             k_degree = k.degree()

src/sage/schemes/curves/affine_curve.py

@@ -2068,6 +2068,7 @@ def _genus(self):
 
         TESTS::
 
+            sage: # needs sage.rings.number_field
             sage: R.<T> = QQ[]
             sage: N.<a> = NumberField(T^2 + 1)
             sage: A2.<x,y> = AffineSpace(N, 2)

src/sage/schemes/curves/constructor.py

@@ -72,9 +72,6 @@
                            IntegralAffinePlaneCurve,
                            IntegralAffinePlaneCurve_finite_field)
 
-_Fields = Fields()
-_NumberFields = NumberFields()
-
 
 def _is_irreducible_and_reduced(F) -> bool:
     """
@@ -312,16 +309,16 @@ def Curve(F, A=None):
             if A.coordinate_ring().ideal(F).is_zero():
                 if isinstance(k, FiniteField):
                     return IntegralAffineCurve_finite_field(A, F)
-                if k in _Fields:
+                if k in Fields():
                     return IntegralAffineCurve(A, F)
                 return AffineCurve(A, F)
             raise TypeError(f"{F} does not define a curve in one-dimensional affine space")
         if n != 2:
             if isinstance(k, FiniteField):
                 if A.coordinate_ring().ideal(F).is_prime():
                     return IntegralAffineCurve_finite_field(A, F)
-            if k in _Fields:
-                if (k == QQ or k in _NumberFields) and A.coordinate_ring().ideal(F).is_prime():
+            if k in Fields():
+                if (k == QQ or k in NumberFields()) and A.coordinate_ring().ideal(F).is_prime():
                     return IntegralAffineCurve(A, F)
                 return AffineCurve_field(A, F)
             return AffineCurve(A, F)
@@ -334,8 +331,8 @@ def Curve(F, A=None):
             if _is_irreducible_and_reduced(F):
                 return IntegralAffinePlaneCurve_finite_field(A, F)
             return AffinePlaneCurve_finite_field(A, F)
-        if k in _Fields:
-            if (k == QQ or k in _NumberFields) and _is_irreducible_and_reduced(F):
+        if k in Fields():
+            if (k == QQ or k in NumberFields()) and _is_irreducible_and_reduced(F):
                 return IntegralAffinePlaneCurve(A, F)
             return AffinePlaneCurve_field(A, F)
         return AffinePlaneCurve(A, F)
@@ -345,7 +342,7 @@ def Curve(F, A=None):
             if A.coordinate_ring().ideal(F).is_zero():
                 if isinstance(k, FiniteField):
                     return IntegralProjectiveCurve_finite_field(A, F)
-                if k in _Fields:
+                if k in Fields():
                     return IntegralProjectiveCurve(A, F)
                 return ProjectiveCurve(A, F)
             raise TypeError(f"{F} does not define a curve in one-dimensional projective space")
@@ -355,8 +352,8 @@ def Curve(F, A=None):
             if isinstance(k, FiniteField):
                 if A.coordinate_ring().ideal(F).is_prime():
                     return IntegralProjectiveCurve_finite_field(A, F)
-            if k in _Fields:
-                if (k == QQ or k in _NumberFields) and A.coordinate_ring().ideal(F).is_prime():
+            if k in Fields():
+                if (k == QQ or k in NumberFields()) and A.coordinate_ring().ideal(F).is_prime():
                     return IntegralProjectiveCurve(A, F)
                 return ProjectiveCurve_field(A, F)
             return ProjectiveCurve(A, F)
@@ -374,8 +371,8 @@ def Curve(F, A=None):
             if _is_irreducible_and_reduced(F):
                 return IntegralProjectivePlaneCurve_finite_field(A, F)
             return ProjectivePlaneCurve_finite_field(A, F)
-        if k in _Fields:
-            if (k == QQ or k in _NumberFields) and _is_irreducible_and_reduced(F):
+        if k in Fields():
+            if (k == QQ or k in NumberFields()) and _is_irreducible_and_reduced(F):
                 return IntegralProjectivePlaneCurve(A, F)
             return ProjectivePlaneCurve_field(A, F)
         return ProjectivePlaneCurve(A, F)

src/sage/schemes/curves/curve.py

@@ -238,17 +238,17 @@ def geometric_genus(self):
             sage: C.geometric_genus()
             3
 
-        Note that the geometric genus is only defined for `geometrically
-        irreducible curve <https://stacks.math.columbia.edu/tag/0BYE>`_. This
-        method does not check the condition. Be warned that you may get a
-        nonsensical result if the curve is not geometrically irreducible.
+        .. WARNING::
 
-        A curve that is not geometrically irreducible::
+            Geometric genus is only defined for `geometrically irreducible curve
+            <https://stacks.math.columbia.edu/tag/0BYE>`_. This method does not
+            check the condition. You may get a nonsensical result if the curve is
+            not geometrically irreducible::
 
-            sage: P2.<x,y,z> = ProjectiveSpace(QQ, 2)
-            sage: C = Curve(x^2 + y^2, P2)
-            sage: C.geometric_genus()  # nonsense!
-            -1
+                sage: P2.<x,y,z> = ProjectiveSpace(QQ, 2)
+                sage: C = Curve(x^2 + y^2, P2)
+                sage: C.geometric_genus()  # nonsense!
+                -1
         """
         try:
             return self._genus