1. Some algebraic consequences of Green’s hyperplane restriction theorems
- Author
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Boij, Mats and Zanello, Fabrizio
- Subjects
- *
ALGEBRAIC geometry , *POTENTIAL theory (Mathematics) , *GORENSTEIN rings , *CHARACTERISTIC functions , *MATHEMATICAL symmetry , *VECTOR fields - Abstract
Abstract: We discuss Green’s paper from a new algebraic perspective, and provide applications of its results to level and Gorenstein algebras, concerning their Hilbert functions and the weak Lefschetz property. In particular, we will determine a new infinite class of symmetric -vectors that cannot be Gorenstein -vectors, which was left open in the recent work . This includes the smallest example, previously unknown, . As M. Green’s results depend heavily on the characteristic of the base field, so will ours. The Appendix contains a new argument, kindly provided to us by M. Green, for Theorems 3 and 4 of , since we had found a gap in the original proof of those results during the preparation of this manuscript. [Copyright &y& Elsevier]
- Published
- 2010
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