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:
“The nearest the modern general or admiral comes to a small-arms encounter of any sort is at a duck hunt in the company of corporation executives at the retreat of Continental Motors, Inc.”
—C. Wright Mills (1916–1962)
“Being in a family is like being in a play. Each birth order position is like a different part in a play, with distinct and separate characteristics for each part. Therefore, if one sibling has already filled a part, such as the good child, other siblings may feel they have to find other parts to play, such as rebellious child, academic child, athletic child, social child, and so on.”
—Jane Nelson (20th century)