Recent content by math2012

A1. Yes A2. Yes A3. No? Not sure. -x2 (x1*x4-x2*x3)+x3 (x1*x3-x2^2)+x1 (x2*x4-x3^2)=0 (*) and -x3 (x1*x4-x2*x3)+x4 (x1*x3-x2^2)+x2 (x2*x4-x3^2)=0 (**) Are (*) and (**) relevant at all?

Never mind in regards to this: "What is the ideal for this example?..." I reread what you wrote and you answered my question. Also, I solved my own original question. Thank you for your time.

> E.g. the union of two planes meeting at a point is not a complete intersection. What is the ideal for this example? An ideal for the first plane and an ideal for the second plane? Are the planes somehow bent (and embedded in some higher dimensional space) so that they're meeting only at a point?

So it seems like you did some reading on Grobner basis, but just in case, here's what it means to be a Grobner basis. A quick background first: let's just say we're in some polynomial ring R with n+N variables (N>0) in some algebraically closed field k and suppose we have imposed some sort of...

Does anyone know if a set of homogeneous polynomials forms a reduced Grobner basis, then they form a regular sequence in the polynomial ring? Any references? All the references that I have looked at (so far) have not related the two. If this is not true, can you give me a counterexample...

When explicitly given a set of polynomial equations, I am interested in describing its singular locus. I read this from several sources that a point is singular if the rank of a Jacobian at a singular point must be any number less than its maximal possible number. Or is it the locus where all...