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Relevant bibliographies by topics / B-divisors

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Academic literature on the topic 'B-divisors'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "B-divisors"

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Boiko, Denys. "Application of Divisors on a Hyperelliptic Curve in Python." Mohyla Mathematical Journal 3 (January 29, 2021): 11–24. http://dx.doi.org/10.18523/2617-70803202011-24.

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The paper studies hyperelliptic curves of the genus g > 1, divisors on them and their applications in Python programming language. The basic necessary definitions and known properties of hyperelliptic curves are demonstrated, as well as the notion of polynomial function, its representation in unique form, also the notion of rational function, norm, degree and conjugate to a polynomial are presented. These facts are needed to calculate the order of points of desirable functions, and thus to quickly and efficiently calculate divisors. The definition of a divisor on a hyperelliptic curve is sh

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Küronya, Alex, and Catriona Maclean. "Zariski decomposition of b-divisors." Mathematische Zeitschrift 273, no. 1-2 (2012): 427–36. http://dx.doi.org/10.1007/s00209-012-1012-1.

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Haukkanen, Pentti, and Varanasi Sitaramaiah. "Bi-unitary multiperfect numbers, IV(b)." Notes on Number Theory and Discrete Mathematics 27, no. 1 (2021): 45–69. http://dx.doi.org/10.7546/nntdm.2021.27.1.45-69.

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A divisor d of a positive integer n is called a unitary divisor if \gcd(d, n/d)=1; and d is called a bi-unitary divisor of n if the greatest common unitary divisor of d and n/d is unity. The concept of a bi-unitary divisor is due to D. Surynarayana (1972). Let \sig^{**}(n) denote the sum of the bi-unitary divisors of n. A positive integer n is called a bi-unitary multiperfect number if \sig^{**}(n)=kn for some k\geq 3. For k=3 we obtain the bi-unitary triperfect numbers. Peter Hagis (1987) proved that there are no odd bi-unitary multiperfect numbers. The present paper is part IV(b) in a series

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Sander, J. W., and T. Sander. "On So's conjecture for integral circulant graphs." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 59–72. http://dx.doi.org/10.2298/aadm150226009s.

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Each integral circulant graph ICG(n,D) is characterised by its order n and a set D of positive divisors of n in such a way that it has vertex set Z=nZ and edge set {(a,b) : a, b ? Z=nZ, gcd(a - b,n) ? D}. According to a conjecture of So two integral circulant graphs are isomorphic if and only if they are isospectral, i.e. they have the same eigenvalues (counted with multiplicities). We prove a weaker form of this conjecture, namely, that two integral circulant graphs with multiplicative divisor sets are isomorphic if and only if their spectral vectors coincide.

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Lesieutre, John. "The diminished base locus is not always closed." Compositio Mathematica 150, no. 10 (2014): 1729–41. http://dx.doi.org/10.1112/s0010437x14007544.

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AbstractWe exhibit a pseudoeffective $\mathbb{R}$-divisor ${D}_{\lambda }$ on the blow-up of ${\mathbb{P}}^{3}$ at nine very general points which lies in the closed movable cone and has negative intersections with a set of curves whose union is Zariski dense. It follows that the diminished base locus ${\boldsymbol{B}}_{-}({D}_{\lambda })={\bigcup }_{A\,\text{ample}}\boldsymbol{B}({D}_{\lambda }+A)$ is not closed and that ${D}_{\lambda }$ does not admit a Zariski decomposition in even a very weak sense. By a similar method, we construct an $\mathbb{R}$-divisor on the family of blow-ups of ${\ma

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Koninck, Jean-Marie de, and Aleksandar Ivić. "On the Distance Between Consecutive Divisors of an Integer." Canadian Mathematical Bulletin 29, no. 2 (1986): 208–17. http://dx.doi.org/10.4153/cmb-1986-034-7.

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AbstractLet ω(n) denote the number of distinct prime divisors of a positive integer n. Then we define and where are primes and r ≥ 2. Similarly denote by the number of divisors of n and let be defined by where are the divisors of n. We prove that there exists constants A and B such that and

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Sander, J. W., and T. Sander. "The energy of integral circulant graphs with prime power order." Applicable Analysis and Discrete Mathematics 5, no. 1 (2011): 22–36. http://dx.doi.org/10.2298/aadm110131003s.

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The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

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Moree, Pieter. "On the divisors of $a^k + b^k$." Acta Arithmetica 80, no. 3 (1997): 197–212. http://dx.doi.org/10.4064/aa-80-3-197-212.

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Agdgomelashvili, Zurab. "Some interesting tasks from the classical number theory." Works of Georgian Technical University, no. 4(518) (December 15, 2020): 150–88. http://dx.doi.org/10.36073/1512-0996-2020-4-150-188.

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The article considers the following issues: – It’s of great interest for p and q primes to determine the number of those prime number divisors of a number 1 1 pq A p    that are less than p. With this purpose we have considered: Theorem 1. Let’s p and q are odd prime numbers and p  2q 1. Then from various individual divisors of the 1 1 pq A p    number, only one of them is less than p. A has at least two different simple divisors; Theorem 2. Let’s p and q are odd prime numbers and p  2q 1. Then all prime divisors of the number 1 1 pq A p    are greater than p; Theorem 3. Let’s q i

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Hashemi, Ebrahim, and Abdollah Alhevaz. "Undirected Zero-Divisor Graphs and Unique Product Monoid Rings." Algebra Colloquium 26, no. 04 (2019): 665–76. http://dx.doi.org/10.1142/s1005386719000488.

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Let R be an associative ring with identity and Z*(R) be its set of non-zero zero-divisors. The undirected zero-divisor graph of R, denoted by Γ(R), is the graph whose vertices are the non-zero zero-divisors of R, and where two distinct vertices r and s are adjacent if and only if rs = 0 or sr = 0. The distance between vertices a and b is the length of the shortest path connecting them, and the diameter of the graph, diam(Γ(R)), is the superimum of these distances. In this paper, first we prove some results about Γ(R) of a semi-commutative ring R. Then, for a reversible ring R and a unique prod

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Dissertations / Theses on the topic "B-divisors"

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Botero, Ana María. "b-divisors on toric and toroidal embeddings." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18140.

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In dieser Dissertation entwickeln wir eine Schnittheorie von torischen bzw. toroidalen b-Divisoren auf torischen bzw. toroidalen Einbettungen. Motiviert wird dies durch das Ziel, eine arithmetische Schnittheorie auf gemischten Shimura- Varietäten von nicht-kompaktem Typ zu begründen. Die bisher zur Verfügung stehenden Werkzeuge definieren keine numerischen Invarianten, die birational invariant sind. Zuerst definieren wir torische b-Divisoren auf torischen Varietäten und einen Integrabilitätsbegriff für solche Divisoren. Wir zeigen, dass torische b-Divisoren unter geeigneten Annahmen an

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Botero, Ana María [Verfasser], and Jürg [Gutachter] Kramer. "b-divisors on toric and toroidal embeddings / Ana María Botero ; Gutachter: Jürg Kramer." Berlin : Humboldt-Universität zu Berlin, 2017. http://d-nb.info/1189328941/34.

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Books on the topic "B-divisors"

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Tretkoff, Paula. Existence of Ball Quotients Covering Line Arrangements. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0007.

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This chapter justifies the assumption that ball quotients covering line arrangements exist. It begins with the general case on the existence of finite covers by ball quotients of weighted configurations, focusing on log-canonical divisors and Euler numbers reflecting the weight data on divisors on the blow-up X of P2 at the singular points of a line arrangement. It then uses the Kähler-Einstein property to prove an inequality between Chern forms that, when integrated, gives the appropriate Miyaoka-Yau inequality. It also discusses orbifolds and b-spaces, weighted line arrangements, the problem

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Voisin, Claire. On the Chow ring of K3 surfaces and hyper-Kahler manifolds. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160504.003.0005.

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This chapter considers varieties whose Chow ring has special properties. This includes abelian varieties, K3 surfaces, and Calabi–Yau hypersurfaces in projective space. For K3 surfaces S, it was discovered that they have a canonical 0-cycle o of degree 1 with the property that the product of two divisors of S is a multiple of o in CH₀(S). This result would later be extended to Calabi–Yau hypersurfaces in projective space. The chapter also considers a decomposition in CH(X × X × X)ℚ of the small diagonal Δ‎ ⊂ X × X × X that was established for K3 surfaces, and is partially extended to Calabi–Ya

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Book chapters on the topic "B-divisors"

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Corti, Alessio, James McKernan, and Hiromichi Takagi. "Saturated mobile b-divisors on weak del Pezzo klt surfaces." In Flips for 3-folds and 4-folds. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780198570615.003.0006.

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Couveignes, Jean-Marc. "Approximating Vf over the complex numbers." In Computational Aspects of Modular Forms and Galois Representations. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691142012.003.0012.

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This chapter addresses the problem of computing torsion divisors on modular curves with an application to the explicit calculation of modular representations. The final result of the chapter is Theorem 12.14.1 (approximating Vsubscript f). It identifies two differences between this Theorem 12.14.1 and Theorem 12.10.7. First, it claims that it can separate the cuspidal and the finite part of Qₓ. Second, it returns algebraic coordinates b and x for the points Qsubscript x,n rather than analytic ones.

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"Appendix B." In Divisors and Sandpiles. American Mathematical Society, 2018. http://dx.doi.org/10.1090/mbk/114/17.

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Higgins, Peter M. "1. Numbers and algebra." In Algebra: A Very Short Introduction. Oxford University Press, 2015. http://dx.doi.org/10.1093/actrade/9780198732822.003.0001.

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‘Numbers and algebra’ introduces the number system and explains several terms used in algebra, including natural numbers, positive and negative integers, rational numbers, number factorization, the Fundamental Theorem of Arithmetic, Euclid’s Lemma, the Division Algorithm, and the Euclidean Algorithm. It proves that any common factor c of a and b is also a factor of any number of the form ax + by, and since the greatest common divisor (gcd) of a and b has this form, which may be found by reversing the steps of the Euclidean Algorithm, it follows that any common factor c of a and b divides their gcd d.

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