The moduli of surfaces admitting genus two fibrations over elliptic curves

Download

index.pdf

Date

2005

Author

Karadoğan, Gülay

Metadata

Show full item record

Item Usage Stats

230
views

96
downloads

In this thesis, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and we employ results on the moduli of polarized elliptic surfaces, to construct moduli spaces of these smooth fibrations. In the case of nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes H(1,X(d),n) of morphisms of degree n from elliptic curves to the modular curve X(d), d=3. Ultimately, we show that the moduli spaces, considered, are fiber spaces over the affine line A¹ with fibers determined by the components of H (1,X(d),n).

Subject Keywords

Algebraic geometry.

URI

http://etd.lib.metu.edu.tr/upload/12606084/index.pdf
https://hdl.handle.net/11511/15106

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Hilbert functions of gorenstein monomial curves Topaloğlu Mete, Pınar; Arslan, Sefa Feza; Department of Mathematics (2005) The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Lat...
Lifting fibrations on algebraic surfaces to characteristic zero Kaya, Celalettin; Önsiper, Mustafa Hurşit; Department of Mathematics (2005) In this thesis, we study the problem of lifting fibrations on surfaces in characteristic p, to characteristic zero. We restrict ourselves mainly to the case of natural fibrations on surfaces with Kodaira dimension -1 or 0. We determine whether such a fibration lifts to characteristic zero. Then, we try to find the smallest ring over which a lifting is possible. Finally,in some favourable cases, we compare the moduli of liftings of the fibration to the moduli of liftings of the surface under consideration.
ON GENERALIZED LOCAL SYMMETRIES OF THE SO(2,1) INVARIANT NONLINEAR SIGMA-MODEL BASKAL, S; ERIS, A; SATIR, A (1994-12-19) The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem Alpay, D; Kaptanoglu, HT (2000-12-15) Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
Finite rigid sets in curve complexes of nonorientable surfaces Ilbira, Sabahattin; Korkmaz, Mustafa (Springer Science and Business Media LLC, 2020-06-01) A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected nonorientable surfaces of genus g with n holes for g + n not equal 4.

Citation Formats

G. Karadoğan, “The moduli of surfaces admitting genus two fibrations over elliptic curves,” Ph.D. - Doctoral Program, Middle East Technical University, 2005.