Geodesic
Piecewise lexsegment ideals
Sbornik. Mathematics, Tome 194 (2003) no. 11, pp. 1701-1724

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The problem of describing the Hilbert functions of homogeneous ideals of a commutative polynomial ring containing a fixed monomial ideal $I$ is considered. For this purpose the notion of a piecewise lexsegment ideal is introduced generalizing the notion of a lexsegment ideal. It is proved that if $I$ is a piecewise lexsegment ideal, then it is possible to describe the Hilbert functions of homogeneous ideals containing $I$ in a way similar to that suggested by Macaulay for the situation $I=0$. Moreover, a generalization of extremal properties of lexsegment ideals is obtained (the inequality for the Betti numbers, behaviour under factorization by homogeneous generic forms). 
@article{SM_2003_194_11_a5,
     author = {D. A. Shakin},
     title = {Piecewise lexsegment ideals},
     journal = {Sbornik. Mathematics},
     pages = {1701--1724},
     publisher = {mathdoc},
     volume = {194},
     number = {11},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_11_a5/}
}
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D. A. Shakin. Piecewise lexsegment ideals. Sbornik. Mathematics, Tome 194 (2003) no. 11, pp. 1701-1724. http://geodesic.mathdoc.fr/item/SM_2003_194_11_a5/