scholarly journals Rational Picard Group of Moduli of Pointed Hyperelliptic Curves

2020 ◽  
Vol 2020 (21) ◽  
pp. 8027-8056
Author(s):  
Federico Scavia
Keyword(s):  
Moduli Spaces ◽  
Class Group ◽  
Hyperelliptic Curves ◽  
Picard Group ◽  
Complex Numbers ◽  
Divisor Class Group ◽  
Divisor Class

Abstract We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne–Mumford compactification, over the field of complex numbers.

scholarly journals Improved divisor arithmetic on generic hyperelliptic curves

2020 ◽  
Vol 54 (3) ◽  
pp. 95-99
Author(s):  
Sebastian Lindner ◽  
Laurent Imbert ◽  
Michael J. Jacobson
Keyword(s):  
Algebraic Geometry ◽  
Hyperelliptic Curve ◽  
Class Group ◽  
Finite Abelian Group ◽  
Hyperelliptic Curves ◽  
Computer Algebra Systems ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Open Questions ◽  
Fast Arithmetic

The divisor class group of a hyperelliptic curve defined over a finite field is a finite abelian group at the center of a number of important open questions in algebraic geometry, number theory and cryptography. Many of these problems lend themselves to numerical investigation, and as emphasized by Sutherland [14, 13], fast arithmetic in the divisor class group is crucial for their efficiency. Besides, implementations of these fundamental operations are at the core of the algebraic geometry packages of widely-used computer algebra systems such as Magma and Sage.

scholarly journals Some factorization properties of Krull domains with infinite cyclic divisor class group

1994 ◽  
Vol 96 (2) ◽  
pp. 97-112 ◽  
Author(s):  
David F. Anderson ◽  
Scott T. Chapman ◽  
William W. Smith
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Krull Domains

scholarly journals The divisor class group of a Quot scheme

2010 ◽  
Vol 3 (0) ◽  
pp. 1-14
Author(s):  
Rafael Hernández ◽  
Daniel Ortega
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Quot Scheme

scholarly journals ON FACTORIZATION IN BLOCK MONOIDS FORMED BY $\{\bar{1},\bar{a}\}$ IN $\mathbb{Z}_{n}$

2003 ◽  
Vol 46 (2) ◽  
pp. 257-267 ◽  
Author(s):  
Scott T. Chapman ◽  
William W. Smith
Keyword(s):  
Class Group ◽  
Subject Classification ◽  
Division Algorithm ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Irreducible Elements ◽  
Complete Set ◽  
Cross Number ◽  
Block Monoids ◽  
Block Monoid

AbstractWe consider the factorization properties of block monoids on $\mathbb{Z}_n$ determined by subsets of the form $S_a=\{\bar{1},\bar{a}\}$. We denote such a block monoid by $\mathcal{B}_a(n)$. In §2, we provide a method based on the division algorithm for determining the irreducible elements of $\mathcal{B}_a(n)$. Section 3 offers a method to determine the elasticity of $\mathcal{B}_a(n)$ based solely on the cross number. Section 4 applies the results of §3 to investigate the complete set of elasticities of Krull monoids with divisor class group $\mathbb{Z}_n$.AMS 2000 Mathematics subject classification: Primary 20M14; 20D60; 13F05

scholarly journals A Theorem About Maximal Cohen–Macaulay Modules

2020 ◽  
Author(s):  
Thomas Polstra
Keyword(s):  
Natural Number ◽  
Regular Ring ◽  
Class Group ◽  
Torsion Subgroup ◽  
Finitely Generated ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Frobenius Endomorphism

Abstract It is shown that for any local strongly $F$-regular ring there exists natural number $e_0$ so that if $M$ is any finitely generated maximal Cohen–Macaulay module, then the pushforward of $M$ under the $e_0$th iterate of the Frobenius endomorphism contains a free summand. Consequently, the torsion subgroup of the divisor class group of a local strongly $F$-regular ring is finite.

scholarly journals The Noether–Lefschetz theorem for the divisor class group

2009 ◽  
Vol 322 (9) ◽  
pp. 3373-3391 ◽  
Author(s):  
G.V. Ravindra ◽  
V. Srinivas
Keyword(s):  
Class Group ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Lefschetz Theorem
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