Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cuspidal plane curves, syzygies and a bound on the MW-rank   Let $C=Z(f)$ be a reduced plane curve of degree $6k$, with only nodes and
ordinary cusps as singularities. Let $I$ be the ideal of the points where $C$
has a cusp. Let $\oplus S(-b_i)\to \oplus S(-a_i) \to S\to S/I$ be a minimal
resolution of $I$. We show that $b_i\leq 5k$. From this we obtain that the
Mordell-Weil rank of the elliptic threefold $W:y^2=x^3+f$ equals $2#\{i\mid
b_i=5k\}$. Using this we find an upper bound for the Mordell-Weil rank of $W$,
which is $1/18 (125+\sqrt{73}-\sqrt{2302-106\sqrt{73}})k+l.o.t.$ and we find an
upper bound for the exponent of $(t^2-t+1)$ in the Alexander polynomial of $C$,
which is $1/36(125+\sqrt{73}-\sqrt{2302-106\sqrt{73}})k+l.o.t.$. This improves
a recent bound of Cogolludo and Libgober almost by a factor 2.

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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat