0
votes
1answer
128 views

Discriminant of a polynomial in two variables

I want to compute the discriminant of the following polynomial $$ F(X,Y)=X^mY^n+\sum_{i=0}^{m-1}\sum_{j=0}^{n-1}c_{ij}X^iY^j. $$ Here the discriminate means the equation $D(c_{i,j})$ in the variables ...
3
votes
1answer
212 views

plane cubics and conic bundles

It is well known that any plane cubic curve can be obtained as the discriminant locus of a conic bundle (actually even just of a net of conics). Does this hold true also for all nodal cubics (with ...
6
votes
2answers
354 views

Parameter space for complete intersections and their discriminant

Consider globally complete intersections in $\mathbb{P}^n$, of codimension $k$, of some fixed multi-degree $(d_1,\dots,d_k)$. Is there some nice (i.e. "explicit") parameter space for them? (even if ...