Topic
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.
Papers published on a yearly basis
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TL;DR: In this article, the Weyl cycles of codimension two were defined on the Mori-dream space and the expected dimension for the space of the global sections of any effective divisor that generalizes the linear expected dimension and the secant expected dimension.
Abstract: We define the Weyl cycles on $X^n_s$, the blown up projective space $\mathbb{P}^n$ in $s$ points in general position. In particular, we focus on the Mori Dream spaces $X^3_7$ and $X^{4}_{8}$, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of the global sections of any effective divisor that generalizes the linear expected dimension and the secant expected dimension.
1 citations
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01 Dec 2019TL;DR: In this paper, it was shown that for every real Galois number field K there exists a smooth projective variety X and a divisor D on X such that X(D) is a primitive element of K.
Abstract: We prove the following result: for every totally real Galois number field K there exists a smooth projective variety X and a divisor D on X such that \(vol_X(D)\) is a primitive element of K.
1 citations
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TL;DR: This paper describes how Nagao's methods, together with a sub-quadratic complexity partial extended Euclidean algorithm using the half-gcd algorithm can be applied to improve arithmetic in the degree zero divisor class group.
Abstract: A significant amount of effort has been devoted to improving divisor
arithmetic on low-genus hyperelliptic curves via explicit versions of generic
algorithms. Moderate and high genus curves also arise in cryptographic
applications, for example, via the Weil descent attack on the elliptic curve
discrete logarithm problem, but for these curves, the generic algorithms are
to date the most efficient available. Nagao [22] described how
some of the techniques used in deriving efficient explicit formulas can be
used to speed up divisor arithmetic using Cantor's algorithm on curves of
arbitrary genus. In this paper, we describe how Nagao's methods, together
with a sub-quadratic complexity partial extended Euclidean algorithm using the
half-gcd algorithm can be applied to improve arithmetic in the degree zero
divisor class group. We present numerical results showing which combination
of techniques is more efficient for hyperelliptic curves over $\mathbb{F}_{2^n}$ of
various genera.
1 citations
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01 Sep 2013
1 citations
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TL;DR: For the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, this article showed that it is generically non-degenerate when X is projective and K_X+D is ample.
Abstract: We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K-correspondences. We define an intrinsic logarithmic pseudo-volume form \Phi_{X,D} for every pair (X,D) consisting of a complex manifold X and a normal crossing Weil divisor, the positive part of which is reduced. We then prove that \Phi_{X,D} is generically non-degenerate when X is projective and K_X+D is ample. This result is analogous to the classical Kobayashi-Ochiai theorem. We also show the vanishing of \Phi_{X,D} for a large class of log-K-trivial pairs, which is an important step in the direction of the Kobayashi conjecture about infinitesimal measure hyperbolicity in the logarithmic case.
1 citations