Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Graded Free Resolutions for Monomial Curves Defined by
  Arithmetic Sequences   Let $\mm=(m_0,...,m_n)$ be an arithmetic sequence, i.e., a sequence of
integers $m_0<...<m_n$ with no common factor that minimally generate the
numerical semigroup $\sum_{i=0}^{n}m_i\N$ and such that
$m_i-m_{i-1}=m_{i+1}-m_i$ for all $i\in\{1,...,n-1\}$. The homogeneous
coordinate ring $\Gamma_\mm$ of the affine monomial curve parametrically
defined by $X_0=t^{m_0},...,X_n=t^{m_n}$ is a graded $R$-module where $R$ is
the polynomial ring $k[X_0,...,X_n]$ with the grading obtained by setting
$\deg{X_i}:=m_i$. In this paper, we construct an explicit minimal graded free
resolution for $\Gamma_\mm$ and show that its Betti numbers depend only on the
value of $m_0$ modulo $n$. As a consequence, we prove a conjecture of Herzog
and Srinivasan on the eventual periodicity of the Betti numbers of semigroup
rings under translation for the monomial curves defined by an arithmetic
sequence.

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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph