scholarly journals Abelian varieties with group action

2004 ◽  
Vol 2004 (575) ◽  
Author(s):  
H. Lange ◽  
S. Recillas
Keyword(s):  
Group Action ◽  
Abelian Varieties

scholarly journals Shimura curves in the Prym loci of ramified double covers

2021 ◽  
Author(s):  
Paola Frediani ◽  
Gian Paolo Grosselli
Keyword(s):  
Computer Algebra ◽  
Group Action ◽  
Abelian Varieties ◽  
Shimura Curves ◽  
One Dimensional ◽  
Fixed Group ◽  
Base Curve ◽  
Double Covers ◽  
Ramification Points

We study Shimura curves of PEL type in the space of polarized abelian varieties [Formula: see text] generically contained in the ramified Prym locus. We generalize to ramified double covers, the construction done in [E. Colombo, P. Frediani, A. Ghigi and M. Penegini, Shimura curves in the Prym locus, Commun. Contemp. Math. 21(2) (2019) 1850009] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is [Formula: see text]. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.

RETRACTED ARTICLE: Abelian varieties with finite abelian group action

2018 ◽  
Vol 112 (4) ◽  
pp. 447-448
Author(s):  
Angel Carocca ◽  
Herbert Lange ◽  
Rubí E. Rodríguez
Keyword(s):  
Abelian Group ◽  
Group Action ◽  
Finite Abelian Group ◽  
Abelian Varieties ◽  
Retracted Article

scholarly journals Abelian varieties with finite abelian group action

2019 ◽  
Vol 112 (6) ◽  
pp. 615-622
Author(s):  
Angel Carocca ◽  
Herbert Lange ◽  
Rubí E. Rodríguez
Keyword(s):  
Abelian Group ◽  
Group Action ◽  
Finite Abelian Group ◽  
Abelian Varieties

scholarly journals Shimura subvarieties in the Prym locus of ramified Galois coverings

2021 ◽  
Author(s):  
Gian Paolo Grosselli ◽  
Abolfazl Mohajer
Keyword(s):  
Computer Algebra ◽  
Group Action ◽  
Moduli Space ◽  
Abelian Varieties ◽  
Fixed Group ◽  
Galois Coverings ◽  
Base Curve ◽  
Prym Map

AbstractWe study Shimura (special) subvarieties in the moduli space $$A_{p,D}$$ A p , D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to $${{\mathbb {P}}}^1$$ P 1 . We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.

Analytic Theory of Abelian Varieties

1974 ◽  
Author(s):  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Abelian Varieties ◽  
Analytic Theory

On the family of Riemann surfaces with tetrahedral group action

2019 ◽  
Vol 42 (3) ◽  
pp. 476-495
Author(s):  
Ryota Hirakawa
Keyword(s):  
Group Action ◽  
Riemann Surfaces ◽  
The Family

scholarly journals Optimized CSIDH Implementation Using a 2-Torsion Point

Cryptography ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 20 ◽  
Author(s):  
Donghoe Heo ◽  
Suhri Kim ◽  
Kisoon Yoon ◽  
Young-Ho Park ◽  
Seokhie Hong
Keyword(s):  
Elliptic Curve ◽  
Group Action ◽  
Large Degree ◽  
Transitive Group ◽  
Optimization Method ◽  
Torsion Point ◽  
Torsion Points ◽  
Diffie Hellman ◽  
Odd Degree ◽  
Montgomery Curve

The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. Because the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) requires odd-degree isogenies up to at least 587, this inefficiency is the main bottleneck of using a Montgomery curve for CSIDH. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH, in which the three rational two-torsion points exist. By using the proposed parameters, the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a two-torsion point. We also proved that the CSIDH while using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.4% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved while only using Montgomery curves.

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

scholarly journals Classification of nonrigid families of abelian varieties

1993 ◽  
Vol 45 (2) ◽  
pp. 159-189
Author(s):  
Masa-Hiko Saitō
Keyword(s):  
Abelian Varieties
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