Browsing by Author "84717609-0bce-4fa3-91da-9e0ce492d391"

Now showing items 1-9 of 9

    • A note on Galois embeddings of abelian varieties 
      Auffarth, Robert (Springer, 2017)
      In this note we show that if an abelian variety possesses a Galois embedding into some projective space, then it must be isogenous to the self product of an elliptic curve. We prove moreover that the self product of an ...
    • Direct image of parabolic line bundles 
      Auffarth, Robert; Biswas, Indranil (Elsevier B.V., 2018)
      © 2017 Elsevier B.V. Given a vector bundle E, on an irreducible projective variety X, we give a necessary and sufficient criterion for E to be a direct image of a line bundle under a surjective étale morphism. The criterion ...
    • Elliptic curves on Abelian varieties 
      Auffarth, Robert Frederick (University of Illinois, 2015)
      Given a principally polarized abelian variety (A, Θ), we give a characterization of all elliptic curves that lie on A in terms of intersection numbers of divisor classes in its N´eron-Severi group.
    • Erratum to: A note on Galois embeddings of abelian varieties (manuscripta mathematica, (2017), 154, 3-4, ... 
      Auffarth, Robert (Springer New York LLC, 2019)
      The original Theorem in the article is revised in this erratum based on a referee’s request.
    • Fixed points of endomorphisms of complex tori 
      Alvarado, Matías; Auffarth, Robert (Elsevier, 2018-08-01)
      We study the asymptotic behavior of the cardinality of the fixed point set of iterates of an endomorphism of a complex torus. We show that there are precisely three types of behavior of this function: it is either an ...
    • Smooth quotients of complex tori by finite groups 
      Auffarth, Robert; Arteche, Giancarlo (Springer Heidelberg, 2020)
      Let T be a complex torus and G a finite group acting on T without translations such that T/G is smooth. Consider the subgroup F <= G generated by elements that have at least one fixed point. We prove that there exists a ...
    • The Gauss map and secants of the Kummer variety 
      Auffarth, Robert; Codogni, Giulio; Salvati Manni, Riccardo (John Wiley, 2019)
      Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four-dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian and ...
    • Theta divisors whose Gauss map has a fiber of positive dimension 
      Auffarth, Robert; Codogni, Giulio (Elsevier, 2020)
      We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor ...
    • Torsion points on theta divisors 
      Auffarth, Robert Frederick; Pirola, Gian Pietro; Manni, Riccardo Salvati (American Mathematical Society, 2017)
      © 2016 American Mathematical Society. Using the irreducibility of a natural irreducible representation of the theta group of an ample line bundle on an abelian variety, we derive a bound for the number of n-torsion points ...