1. CJM Online first
||Degrees of regular sequences with a symmetric group action|
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.
Keywords:Complete intersection, symmetric group, regular sequences
Categories:13A02, 13A50, 20C30
2. CJM 2016 (vol 69 pp. 241)
||Finite Determinacy and Stability of Flatness of Analytic Mappings|
It is proved that flatness of an analytic mapping germ from a
complete intersection is determined by its sufficiently high
jet. As a consequence, one obtains finite determinacy of complete
intersections. It is also shown that flatness and openness are
stable under deformations.
Keywords:finite determinacy, stability, flatness, openness, complete intersection
Categories:58K40, 58K25, 32S05, 58K20, 32S30, 32B99, 32C05, 13B40
3. CJM 2012 (vol 64 pp. 1222)
||Normality of Maximal Orbit Closures for Euclidean Quivers|
Let $\Delta$ be an Euclidean quiver. We prove that the closures of
the maximal orbits in the varieties of representations of $\Delta$
are normal and Cohen--Macaulay (even complete intersections).
Moreover, we give a generalization of this result for the tame
Keywords:normal variety, complete intersection, Euclidean quiver, concealed-canonical algebra