Open Problems on Syzygies and Hilbert Functions
نویسندگان
چکیده
منابع مشابه
August 2008 OPEN PROBLEMS on SYZYGIES and HILBERT FUNCTIONS
In this paper we list a number of open problems and conjectures on Hilbert functions and syzygies. Some of the problems are closely related to Algebraic Geometry, Combinatorics, and Hyperplane Arrangements Theory. Our aim is to stimulate interest, rather than to give a complete survey. When describing a problem, we sometimes state one or two related results, and give pointers to a few reference...
متن کاملSYZYGIES 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...
متن کاملMarch 2007 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...
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This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectors of reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction The...
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2009
ISSN: 1939-2346
DOI: 10.1216/jca-2009-1-1-159