Chinese syzygies by insertions

Multisymmetric syzygies

Inspired by the theory of trace identities of matrices, we introduce a very simple approach to the algebra of multisymmetric functions, yielding both generators and relations in an explicit form under the assumption that the order of the symmetric group is invertible in the base field. The method works on the multilinear level regardless of the characteristic. As an application, a consequence i...

NEPHROPATHY CAUSED BY CHINESE HERBS IN IRAN

SYZYGIES and HILBERT FUNCTIONS

Throughout k stands for a field. For simplicity, we assume that k is algebraically closed and has characteristic 0. However, many of the open problems and conjectures make sense without these assumptions. The polynomial ring S = k[x1, . . . , xn] is graded by deg(xi) = 1 for all i. A polynomial f is homogeneous if f ∈ Si for some i, that is, if all monomial terms of f have the same degree. An i...

Three Themes of Syzygies

We present three exciting themes of syzygies, where major progress has been made recently: Boij-Söderberg theory, Stillman’s question, and syzygies over complete intersections. Free resolutions are both central objects and fruitful tools in commutative algebra. They have many applications in algebraic geometry, computational algebra, invariant theory, hyperplane arrangements, mathematical physi...

On Syzygies of Projective

In this article, we give a criterion for an embedding of a projective variety to be deened by quadratic equations and for it to have linear syzygies. Our criterion is intrinsic in nature and implies that embedding corresponding to a suuciently high power of any ample line bundle will have linear syzygies up to a given order. Introduction. Let X be a projective variety. The conditions that guara...