General Position
For more refined questions, the nature of the intersection has to be addressed more closely. The hypersurfaces may be required to satisfy a transversality condition (like their tangent spaces being in general position at intersection points). The intersection may be scheme-theoretic, in other words here the homogeneous ideal generated by the Fi(X0, ..., Xn) may be required to be the defining ideal of V, and not just have the correct radical. In commutative algebra, the complete intersection condition is translated into regular sequence terms, allowing the definition of local complete intersection, or after some localization an ideal has defining regular sequences.
Read more about this topic: Complete Intersection
Famous quotes containing the words general and/or position:
“It was the words “descended into Hades”
That seemed too pagan to our liberal youth.
You know they suffered from a general onslaught.
And well, if they weren’t true why keep right on
Saying them like the heathen? We could drop them.”
—Robert Frost (1874–1963)
“We say that someone occupies an official position, whereas it is the official position that occupies him.”
—G.C. (Georg Christoph)