Cubic curves and totally geodesic subvarieties of moduli space
نویسندگان
چکیده
In this paper we present the first example of a primitive, totally geodesic subvariety F ⊂ Mg,n with dim(F ) > 1. The variety we consider is a surface F ⊂M1,3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in M4, and new SL2(R)–invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.
منابع مشابه
Special Curves and Postcritically Finite Polynomials
We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier...
متن کاملParametrizing Shimura Subvarieties of A1 Shimura Varieties and Related Geometric Problems
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b = (H ) × (H). A special case describes all Shimura subvarieties of type A1 Shimura varieties. We produce, for any n ≥ 1, examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura sub...
متن کاملTotally Geodesic Submanifolds of Teichmüller Space
Main results. Let Tg,n andMg,n denote the Teichmüller and moduli space respectively of genus g Riemann surfaces with n marked points. The Teichmüller metric on these spaces is a natural Finsler metric that quantifies the failure of two different Riemann surfaces to be conformally equivalent. It is equal to the Kobayashi metric [Roy74], and hence reflects the intrinsic complex geometry of these ...
متن کاملEXISTENCE OF CLOSED GEODESICS ON THE MODULI SPACE OF k-MONOPOLES
We establish the existence of non-constant closed geodesics on moduli spaces of SU(2) monopoles of arbitrary charge. More generally, we show that the moduli space of strongly centred monopoles of charge k, k 2, contains a totally geodesic submanifold which can be identiied with the moduli space of strongly centred 2-monopoles for even k's and with the moduli space of centred 2-monopoles for odd...
متن کاملRicci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
متن کامل