Macaulay dual generators of complete intersection ideals defined by complete homogeneous symmetric polynomials of successive degrees

抄録

In this paper, we describe the contraction-annihilated Macaulay dual generators for complete intersection ideals defined by complete homogeneous symmetric polynomials of successive degrees. We also provide the first syzygy of the associated graded ring of each of these complete intersections with respect to the last variable. Using this, we prove that each of these complete intersections possesses the strong Lefschetz property, provided that the coefficient field of the polynomial ring has characteristic 0.