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Ordinary Curves, Webs and the Ubiquity of the Weak Lefschetz Property

✍ Scribed by Miró-Roig, Rosa M.


Book ID
121594553
Publisher
Springer Netherlands
Year
2013
Tongue
English
Weight
310 KB
Volume
17
Category
Article
ISSN
1386-923X

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Let d1; : : : ; dr be positive integers and let I = (F1; : : : ; Fr) be an ideal generated by forms of degrees d1; : : : ; dr, respectively, in a polynomial ring R with n variables. With no further information virtually nothing can be said about I , even if we add the assumption that R=I is Artinian

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Let A = i 0 A i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element of degree 1 such that the multiplication × : A i → A i+1 has maximal rank, for every i, and A has the Strong Lefschetz property if × d : A i → A i+d has maximal ra