Relative Jacobians of Elliptic Fibrations with Reducible Fibers
نویسنده
چکیده
We prove that if X and S are smooth varieties and f : X → S is an elliptic fibration with singular fibers curves of types IN with N ≥ 1, II, III and IV, then the relative Jacobian f̂ : MX/S → S of f , defined as the relative moduli space of semistable pure dimension one sheaves of rank 1 and degree 0 on the fibers of f , is an elliptic fibration such that all its fibers are irreducible. This extends known results when fibers are integral or of type I2.
منابع مشابه
Elliptic Fibrations on a Generic Jacobian Kummer Surface
We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the ...
متن کاملSimpson Jacobians of Reducible Curves
For any projective curve X let M d (X) be the Simpson moduli space of pure dimension one rank 1 degree d sheaves that are semistable with respect to a fixed polarization H on X . When X is a reduced curve the connected component of M d (X) that contains semistable line bundles can be considered as the compactified Jacobian of X . In this paper we give explicitly the structure of this compactifi...
متن کاملOn the Holomorphicity of Genus Two Lefschetz Fibrations
We prove that any genus-2 Lefschetz fibration without reducible fibers and with “transitive monodromy” is holomorphic. The latter condition comprises all cases where the number of singular fibers μ ∈ 10N is not congruent to 0 modulo 40. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in Sbundles over S, of relative degree ≤ 7 over the base, and of sym...
متن کاملClassification of All Jacobian Elliptic Fibrations on Certain K3 Surfaces
In this paper we classify all configurations of singular fibers of elliptic fibrations on the double cover of P ramified along six lines in general position.
متن کاملOn The Moduli of Surfaces Admitting Genus Two Fibrations Over Elliptic Curves
In this paper, 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004