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.
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TL;DR: In this article, an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic curve, or a Z-dense D-integral point set, provided that everything is defined over a number field is presented.
Abstract: We deal with the distributions of holomorphic curves and integral points off divisors. We will simultaneouly prove an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic curve, or a Zariski dense D-integral point set, provided that in the latter case everything is defined over a number field. Then, if the number of components of D is large, the estimate leads to the constancy of such a holomorphic curve or the finiteness of such an integral point set. At the begining, we extend logarithmic Bloch-Ochiai's Theorem to the Kaehler case.
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TL;DR: In this article, the authors give an explicit description of the minimal embedded resolution of the pair of monic irreducible polynomial polynomials corresponding to the special fiber of a special fiber.
Abstract: Let $K$ be a discretely valued field with ring of integers $\mathcal{O}_K$ with perfect residue field. Let $K(x)$ be the rational function field in one variable. Let $\mathbb{P}^1_{\mathcal{O}_K}$ be the standard smooth model of $\mathbb{P}^1_K$ with coordinate $x$ on irreducible special fiber. Let $f(x) \in \mathcal{O}_K[x]$ be a monic irreducible polynomial with corresponding divisor of zeroes $\text{div}_0(f)$ on $\mathbb{P}^1_{\mathcal{O}_K}$. We give an explicit description of the minimal embedded resolution $\mathcal{Y}$ of the pair $(\mathbb{P}^1_{\mathcal{O}_K}, \text{div}_0(f))$ by using Mac Lane's theory to write down the discrete valuations on $K(x)$ corresponding to the irreducible components of the special fiber of $\mathcal{Y}$.
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TL;DR: In this article, the authors studied the growth order of the Cartan subgroup of the Cuspidal Divisor Class Group of the modular curves associated to the normalizer.
Abstract: Let $ \mathfrak{C}^+_{ns}(p) $ be the Cuspidal Divisor Class Group of the modular curves $X^+_{ns}(p) $ associated to the normalizer of a non-split Cartan subgroup of level $ p$. I study the $ p-$primary part of $ \mathfrak{C}^+_{ns}(p) $ and estimate the order of growth of $ |\mathfrak{C}^+_{ns}(p)| $.
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TL;DR: In this article, the authors give a natural stratification of this boundary and show that an iterated blow-up along these strata (or its proper transformations) to obtain a compactification of $M{d}^{\circ}(¶^n)$ with normal crossing divisors.
Abstract: Let $M_{d}(¶^r)$ be the space of $(r+1)$-tuples $(f_0,...,f_r)$ modulo homothety, where $f_0,...,f_r$ are homogeneous polynomials of degree $d$ in two variables. Let $M_{d}^{\circ}(¶^r)$ be the open subset of $M_{d}(¶^r)$ such that $f_0,...,f_r$ have no common zeros. Then $M_{d}^{\circ}(¶^r)$ parametrizes the space of holomorphic maps of degree $d$ from $¶^1$ into $¶^r$. In general the boundary divisor $M_{d}(¶^r) \setminus M_{d}^{\circ}(¶^r)$ is not normal crossing. In this paper we will give a natural stratification of this boundary and show that we can process an iterated blow-ups along these strata (or its proper transformations) to obtain a compactification of $M_{d}^{\circ}(¶^n)$ with normal crossing divisors.
01 Jan 2018
TL;DR: An asymptotic divisor on a spectral curve Σ is said to be of finite type, if the following conditions hold: as mentioned in this paper ] and Σ ≥ 0.
Abstract: An asymptotic divisor \(\mathscr {D}\) on a spectral curve Σ is said to be of finite type, if the following conditions hold: