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, a permutation basis for the cycle class of the moduli space of the divisor class group of $\overline{\mathcal{M}}_{0,n}$ is given.
Abstract: The moduli space $\overline{\mathcal{M}}_{0,n}$ carries a codimension-$d$ cycle class $\kappa_{d}$ We consider the subspace $\mathcal{K}^{d}_{n}$ of $A^d(\overline{\mathcal{M}}_{0,n},\mathbb{Q})$ spanned by pullbacks of $\kappa_d$ via forgetful maps We find a permutation basis for $\mathcal{K}^{d}_{n}$, and describe its annihilator under the intersection pairing in terms of $d$-dimensional boundary strata As an application, we give a new permutation basis of the divisor class group of $\overline{\mathcal{M}}_{0,n}$
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16 Dec 2009
TL;DR: For the moduli space of stable pointed rational curves, this article showed that a divisor non-negatively intersecting all F-curves is linearly equivalent to an effective sum of boundary divisors.
Abstract: Fulton's conjecture for the moduli space of stable pointed rational curves, \bar{M}_{0,n}, claims that a divisor non-negatively intersecting all F-curves is linearly equivalent to an effective sum of boundary divisors. Our main result is a proof of Fulton's conjecture for n=7. A key ingredient in the proof is an \binom{n}{4} dimensional-subspace of the Neron-Severi space of \bar{M}_{0,n}, defined by averages of Keel relations, for which we prove Fulton's conjecture for all n.
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01 Dec 2013
TL;DR: In this paper, the error term of the summatory function of the exponential totient function was studied for the four-dimensional divisor problem of $(a,b,c,c)$ type.
Abstract: In this paper we study the four-dimensional divisor problem of $(a,b,c,c)$ type, where $1\leq a\leq b
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TL;DR: In this paper, it was shown that there are infinitely many primes $p$ such that $p-1$ is divisible by a square $d^2 \geq p^\theta$ for 1/2+1/2000.
Abstract: We show that there are infinitely many primes $p$ such that $p-1$ is divisible by a square $d^2 \geq p^\theta$ for $\theta=1/2+1/2000.$ This improves the work of Matomaki (2009) who obtained the result for $\theta=1/2-\varepsilon$ (with the added constraint that $d$ is also a prime), which improved the result of Baier and Zhao (2006) with $\theta=4/9-\varepsilon.$ Similarly as in the work of Matomaki, we apply Harman's sieve method to detect primes $p \equiv 1 \, (d^2)$. To break the $\theta=1/2$ barrier we prove a new bilinear equidistribution estimate modulo smooth square moduli $d^2$ by using a similar argument as Zhang (2014) used to obtain equidistribution beyond the Bombieri-Vinogradov range for primes with respect to smooth moduli. To optimize the argument we incorporate technical refinements from the Polymath project (2014). Since the moduli are squares, the method produces complete exponential sums modulo squares of primes which are estimated using the results of Cochrane and Zheng (2000).