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:
“As to the rout that is made about people who are ruined by extravagance, it is no matter to the nation that some individuals suffer. When so much general productive exertion is the consequence of luxury, the nation does not care though there are debtors in gaol; nay, they would not care though their creditors were there too.”
—Samuel Johnson (1709–1784)
“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)