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- W4366835637 abstract "Let $A={a_0,ldots,a_{n-1}}$ be a finite set of $ngeq 4$ non-negative relatively prime integers such that $0=a_0<a_1<cdots<a_{n-1}=d$. The $s$-fold sumset of $A$ is the set $sA$ of integers that contains all the sums of $s$ elements in $A$. On the other hand, given an infinite field $k$, one can associate to $A$ the projective monomial curve $mathcal{C}_A$ parametrized by $A$, [ mathcal{C}_A={(v^d:u^{a_1}v^{d-a_1}:cdots :u^{a_{n-2}}v^{d-a_{n-2}}:u^d) mid (u:v)inmathbb{P}^{1}_k}subsetmathbb{P}^{n-1}_k,. ] The exponents in the previous parametrization of $mathcal{C}_A$ define a homogeneous semigroup $mathcal{S}subsetmathbb{N}^2$. We provide several results relating the Castelnuovo-Mumford regularity of $mathcal{C}_A$ to the behaviour of the sumsets of $A$ and to the combinatorics of the semigroup $mathcal{S}$ that reveal a new interplay between commutative algebra and additive number theory." @default.
- W4366835637 created "2023-04-25" @default.
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- W4366835637 date "2023-04-21" @default.
- W4366835637 modified "2023-10-16" @default.
- W4366835637 title "Castelnuovo-Mumford regularity of projective monomial curves via sumsets" @default.
- W4366835637 doi "https://doi.org/10.1007/s00009-023-02482-3" @default.
- W4366835637 hasPublicationYear "2023" @default.
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