Results 11 to 20 of about 2,842 (71)
Geometry of Prym semicanonical pencils and an application to cubic threefolds
Mathematische Nachrichten, Volume 296, Issue 7, Page 2918-2941, July 2023., 2023 Abstract In the moduli space Rg$\mathcal {R}_g$ of double étale covers of curves of a fixed genus g, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors Tge$\mathcal {T}^e_g$ and Tgo$\mathcal {T}^o_g$.
Martí Lahoz +2 more
wiley +1 more source
Motives of moduli spaces of bundles on curves via variation of stability and flips
Journal of the London Mathematical Society, Volume 108, Issue 1, Page 1-53, July 2023., 2023 Abstract We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a choice of stability condition given by weights; our approach is to use explicit descriptions of variation of ...
Lie Fu +2 more
wiley +1 more source
The trigonal construction in the ramified case
Bulletin of the London Mathematical Society, Volume 55, Issue 2, Page 777-792, April 2023., 2023 Abstract To every double cover ramified in two points of a general trigonal curve of genus g$g$, one can associate an étale double cover of a tetragonal curve of genus g+1$g+1$. We show that the corresponding Prym varieties are canonically isomorphic as principally polarized abelian varieties.
Herbert Lange, Angela Ortega
wiley +1 more source
Bounds on the number of rational points of curves in families
Bulletin of the London Mathematical Society, Volume 55, Issue 2, Page 1019-1032, April 2023., 2023 Abstract In this note, we give an alternative proof of uniform boundedness of the number of integral points of smooth projective curves over a fixed number field with good reduction outside of a fixed set of primes. We use that due to Bertin–Romagny, the Kodaira–Parshin families constructed by Lawrence–Venkatesh can themselves be assembled into a ...
Pedro Lemos, Alex Torzewski
wiley +1 more source
sl(2)$\mathfrak {sl}(2)$‐Type singular fibres of the symplectic and odd orthogonal Hitchin system
Journal of Topology, Volume 15, Issue 1, Page 1-38, March 2022., 2022 Abstract We define and parametrize so‐called sl(2)$\mathfrak {sl}(2)$‐type fibres of the Sp(2n,C)$\mathsf {Sp}(2n,\mathbb {C})$‐ and SO(2n+1,C)$\mathsf {SO}(2n+1,\mathbb {C})$‐Hitchin system. These are (singular) Hitchin fibres, such that spectral curve establishes a 2‐sheeted covering of a second Riemann surface Y$Y$.
Johannes Horn
wiley +1 more source
Families of curves with Higgs field of arbitrarily large kernel
Bulletin of the London Mathematical Society, Volume 53, Issue 2, Page 493-506, April 2021., 2021 Abstract In this article, we consider the flat bundle U and the kernel K of the Higgs field naturally associated to any (polarized) variation of Hodge structures of weight 1. We study how strict the inclusion U⊆K can be in the geometric case. More precisely, for any smooth projective curve C of genus g⩾2 and any r=0,…,g−1, we construct non‐isotrivial ...
Víctor González‐Alonso, Sara Torelli
wiley +1 more source
Complete moduli of cubic threefolds and their intermediate Jacobians
Proceedings of the London Mathematical Society, Volume 122, Issue 2, Page 259-316, February 2021., 2021 Abstract The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds.
Sebastian Casalaina‐Martin +3 more
wiley +1 more source
Degenerations of Prym varieties [PDF]
, 2001 Let $(C,\iota)$ be a stable curve with an involution. Following a classical construction one can define its Prym variety $P$, which in this case turns out to be a semiabelian group variety and usually not complete.
V. Alexeev, C. Birkenhake, K. Hulek
semanticscholar +1 more source
Numerical computation of endomorphism rings of Jacobians [PDF]
The Open Book Series, 2018 We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be ...
Nils Bruin +2 more
semanticscholar +1 more source
The rational points on certain Abelian varieties over function fields [PDF]
Journal of Number Theory, 2017 In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we prove a structure
Sajad Salami
semanticscholar +1 more source