Gunnar Fløystad, Bergen: Rigid ideals by deforming letterplace ideals
Abstract: Given a finite poset P, we form the polynomial ring k[xp,yp]p∈P , and the monomial ideal L(2,P) generated by monomials xpyq. (These ideals are precisely those edge ideals of bipartite graphs, which are Cohen-Macaulay ideals.) We get a complete understanding of all polynomial ideals which specialize to the monomial ideal L(2,P), when the Hasse diagram of P is a rooted tree:
- The deformations of L(2,P) are unobstructed
- We compute explicitly the full deformation ideal J(2,P) of L(2,P).
- The full deformation family has a polynomial ring as a base ring.
- The ideal J(2,P) defining the full deformation ideal, is rigid.
- When these ideals are on a Hilbert scheme they are smooth points, and we describe the general point on the Hilbert scheme.
- In simple example cases J(2,P) is the ideal of maximal minors of a generic matrix, and the Pfaffians of a skew-symmetric matrix.
This is joint work with Amin Nematbakhsh.