Results 21 to 30 of about 133 (127)
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
Maximal gonality on strata of differentials and uniruledness of strata in low genus
Bulletin of the London Mathematical Society, Volume 53, Issue 6, Page 1627-1635, December 2021., 2021 Abstract We prove that for a generic element in a nonhyperelliptic component of an abelian stratum Hg(μ) in genus g, the underlying curve has maximal gonality. We extend this result to the case of quadratic strata when the partition μ has positive entries. As a consequence we deduce that all nonhyperelliptic components of H9(μ) are uniruled when μ is a
Andrei Bud
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
Twist-field representations of W-algebras, exact conformal blocks and character identities
Journal of High Energy Physics, 2018 We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial identities involving ...
M. Bershtein +2 more
doaj +1 more source
Products of Jacobians as Prym-Tyurin varieties [PDF]
Geometriae Dedicata, 2008 Let $X_1, ..., X_m$ denote smooth projective curves of genus $g_i \geq 2$ over an algebraically closed field of characteristic 0 and let $n$ denote any integer at least equal to $1+\max_{i=1}^m g_i$. We show that the product $JX_1 \times ... \times JX_m$ of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent ...
Carocca Becerra, Ángel Denys +3 more
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PRYM VARIETIES AND THE INFINITE GRASSMANNIAN [PDF]
International Journal of Mathematics, 1998 In this paper we study Prym varieties and their moduli space using the well-known techniques of the infinite Grassmannian. There are three main results of this paper: a new definition of the BKP hierarchy over an arbitrary base field (that generalizes the classical one over [Formula: see text]); a characterization of Prym varieties in terms of ...
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Polarizations of Prym varieties of pairs of coverings [PDF]
Archiv der Mathematik, 2006 To any pair of coverings $f_i: X \ra X_i, i = 1,2$ of smooth projective curves one can associate an abelian subvariety of the Jacobian $J_X$, the Prym variety $P(f_1,f_2)$ of the pair $(f_1,f_2)$. In some cases we can compute the type of the restriction of the canonical principal polarization of $JX$.
Lange, H., Recillas, S.
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Prym varieties and Teichmüller curves [PDF]
Duke Mathematical Journal, 2006 A Teichmüller curve \(V \subset M_{g}\) is a totally geodesic algebraic curve in the moduli space of Riemann surfaces of genus \(g.\) We say \(V\) is primitive if it is generated by an abelian differential of minimal genus. Every Teichmüller curves has a unique primitive representative in its commensurability class.
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A characterization of Prym varieties [PDF]
International Mathematics Research Notices, 2006 We prove that Prym varieties of algebraic curves with two smooth fixed points of involution are exactly the indecomposable principally polarized abelian varieties whose theta-functions provide explicit formulae for integrable 2D Schrödinger equation.
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Ordinary and almost ordinary Prym varieties [PDF]
Asian Journal of Mathematics, 2019 We study the $p$-rank stratification of the moduli space of Prym varieties in characteristic $p > 0$. For arbitrary primes $p$ and $\ell$ with $\ell \not = p$ and integers $g \geq 3$ and $0 \leq f \leq g$, the first theorem generalizes a result of Nakajima by proving that the Prym varieties of all the unramified ${\mathbb Z}/\ell$-covers of a ...
Ozman, Ekin, Pries, Rachel
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