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Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.


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TL;DR: In this paper, the degree of generation and relations of canonical rings of arbitrary stacky divisors on projective spaces of all dimensions and Hirzebruch surfaces were studied.
Abstract: We give bounds on the degree of generation and relations of canonical rings of arbitrary $\mathbb{Q}$-divisors on projective spaces of all dimensions and Hirzebruch surfaces. We also give exact bounds on the degree of generators and relations of the canonical ring of any effective stacky divisor on projective space.
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TL;DR: For an order embedding of a partially ordered group G into an l-group Γ a topology is introduced on Γ which is defined by a family of valuations W on G.
Abstract: For an order embedding \(G\mathop \to \limits^h \;\Gamma \) of a partly ordered group G into an l-group Γ a topology ’ is introduced on Γ which is defined by a family of valuations W on G. Some density properties of sets h(G), h(Xt) and \((h(X_t )\backslash \{ h(g_1 ),\;.\;.\;.\;,h(g_n )\} )\) (Xt being t-ideals in G) in the topological space ’ are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.
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TL;DR: In this paper, the Kodaira dimension of a smooth projective surface over the complex number field was shown to be 2q(X)-4, where q(X) is the irregularity of the surface.
Abstract: Let $X$ be a smooth projective surface over the complex number field and let $L$ be a nef-big divisor on $X$. Here we consider the following conjecture; If the Kodaira dimension $\kappa(X)\geq 0$, then $K_{X}L\geq 2q(X)-4$, where $q(X)$ is the irregularity of $X$. In this paper, we prove that this conjecture is true if (1) the case in which $\kappa(X)=0$ or 1, (2) the case in which $\kappa(X)=2$ and $h^{0}(L)\geq 2$, or (3) the case in which $\kappa(X)=2$, $X$ is minimal, $h^{0}(L)=1$, and $L$ satisfies some conditions.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140