Complete Intersection - General Position

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:

    In communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic.
    Karl Marx (1818–1883)

    The first full-fledged generation of women in the professions did not talk about their overbooked agenda or the toll it took on them and their families. They knew that their position in the office was shaky at best. . . . If they suffered self-doubt or frustration . . . they blamed themselves—either for expecting too much or for doing too little.
    Deborah J. Swiss (20th century)