Semistable K3-surfaces with icosahedral symmetry
نویسنده
چکیده
In a Type III degeneration of K3-surfaces the dual graph of the central fibre is a triangulation of S2. We realise the tetrahedral, octahedral and especially the icosahedral triangulation in families of K3-surfaces, preferably with the associated symmetry groups acting.
منابع مشابه
Elliptic Fibrations of Some Extremal Semi-stable K3 Surfaces
This paper presents explicit equations over Q for 32 extremal semistable elliptic K3 surfaces. They are realized as pull-back of non-semi-stable extremal rational elliptic surfaces via base change. Together with work of J. Top and N. Yui which exhibited the same procedure for the semi-stable extremal rational elliptic surfaces, this exhausts this approach to produce extremal semi-stable ellipti...
متن کاملDegenerations of K3 Surfaces of Degree Two
Recall. Let π : X → ∆ be a semistable degeneration of K3 surfaces (i.e. a proper, flat, surjective morphism π : X → ∆ whose general fibre Xt = π−1(t) for t ∈ ∆∗ = ∆ − {0} is a smooth K3 surface, such that X is smooth and X0 := π −1(0) is reduced with normal crossings). Then Kulikov [Kul77] [Kul81] and Persson-Pinkham [PP81] show that we can perform birational modifications that affect only the ...
متن کاملModuli stacks and invariants of semistable objects on K3 surfaces
For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T.Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D.Joyce’s work, we introduce the invariants countin...
متن کاملIntroduction to Deformation Theory
We give an introduction to deformation theory with a special focus on the moduli space of semistable sheaves and the Quot-scheme. These are notes to a talk given during Spring 2016 at the graduate seminar on moduli of sheaves on K3 surfaces joint between MIT and NEU.
متن کاملMiranda-persson’s Problem on Extremal Elliptic K3 Surfaces
In one of their early works, Miranda and Persson have classified all possible configurations of singular fibers for semistable extremal elliptic fibrations on K3 surfaces. They also obtained the Mordell-Weil groups in terms of the singular fibers except for 17 cases where the determination and the uniqueness of the groups were not settled. In this paper, we settle these problems completely. We ...
متن کامل