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:
“I have never looked at foreign countries or gone there but with the purpose of getting to know the general human qualities that are spread all over the earth in very different forms, and then to find these qualities again in my own country and to recognize and to further them.”
—Johann Wolfgang Von Goethe (1749–1832)
“Journalism without a moral position is impossible. Every journalist is a moralist. It’s absolutely unavoidable. A journalist is someone who looks at the world and the way it works, someone who takes a close look at things every day and reports what she sees, someone who represents the world, the event, for others. She cannot do her work without judging what she sees.”
—Marguerite Duras (b. 1914)