Stable Morphisms to Singular Schemes and Relative Stable Morphisms

Stable Morphisms to Singular Schemes and Relative Stable Morphisms

Let W/C be a degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first construct the stack of expanded degenerations of W . We then construct the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to W/C. Using a similar technique, for a pair (Z,D) of smooth v...

A Degeneration of Stable Morphisms and Relative Stable Morphisms

Let W → C be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of W . We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to W/C. Using similar technique, for a pair of smooth varie...

Open String Instantons and Relative Stable Morphisms

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a hol...

Binary Morphisms with Stable Suffix Complexity

Let g, h be marked morphisms of words. A pair (g1, h1) of marked morphisms is called a successor of (g, h) if g ◦ g1(a) = h ◦ h1(a) and g ◦ g1(b) = h ◦ h1(b) and the images of g1 and h1 are shortest possible. Successors play an important role in studying the Post Correspondence Problem. Typically, they are simpler than the original morphisms, measured by the number of suffixes of their images (...

Morphisms of Schemes