Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideals of general forms and the ubiquity of the Weak Lefschetz property   Let $d_1,...,d_r$ be positive integers and let $I = (F_1,...,F_r)$ be an
ideal generated by general forms of degrees $d_1,...,d_r$, respectively, in a
polynomial ring $R$ with $n$ variables. When all the degrees are the same we
give a result that says, roughly, that they have as few first syzygies as
possible. In the general case, the Hilbert function of $R/I$ has been
conjectured by Fr\"oberg. In a previous work the authors showed that in many
situations the minimal free resolution of $R/I$ must have redundant terms which
are not forced by Koszul (first or higher) syzygies among the $F_i$ (and hence
could not be predicted from the Hilbert function), but the only examples came
when $r=n+1$. Our second main set of results in this paper show that further
examples can be obtained when $n+1 \leq r \leq 2n-2$. We also show that if
Fr\"oberg's conjecture on the Hilbert function is true then any such redundant
terms in the minimal free resolution must occur in the top two possible degrees
of the free module. Related to the Fr\"oberg conjecture is the notion of Weak
Lefschetz property. We continue the description of the ubiquity of this
property. We show that any ideal of general forms in $k[x_1,x_2,x_3,x_4]$ has
it. Then we show that for certain choices of degrees, any complete intersection
has it and any almost complete intersection has it. Finally, we show that most
of the time Artinian ``hypersurface sections'' of zeroschemes have it.

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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph