arXiv subjects

Karl Fredrickson

Publications and source records attributed to Karl Fredrickson.

4 recordsLinked to original sources

arXiv2015

Resolution of degenerate mirror families via toric morphisms

This paper continues the study of two examples of extremal transitions between families of Calabi-Yau threefolds. In a previous paper we suggested that the "mirror transition" between mirror families predicted by Morrison could be achieved naturally by combining a toric morphism with the Batyrev-Borisov construction. This was carried out for a particular example of a conifold transition. In this paper we show that similar methods work for another extremal transition involving more complicated singularities. We also study how the resolution is related to geometry of the ambient toric varieties, and discuss the connection with recent work by Doran and Harder.

math.AG↗

arXiv2015

Generalized compactifications of Batyrev hypersurface families

We show how Calabi-Yau hypersurface families arising from Batyrev's construction can be resolved and compactified using a type of fan more general than an MPCP resolution. This can lead to smooth projective compactifications that are not obtainable from the original construction. In the threefold case, we show that generic members of the resulting family are always smooth.

math.AG↗

arXiv2014

Mirror Transitions and the Batyrev-Borisov construction

We consider examples of extremal transitions between families of Calabi-Yau complete intersection threefolds in toric varieties, which are induced by toric embeddings of one toric variety into the other. We show that the toric map induced by the linear dual of the embedding induces a birational morphism between the mirror Calabi-Yau families, and in one case show that it can be extended to the full mirror transition between mirror families. Note: this version uses a different approach to give a shorter proof of the same result. Also, Lemma 5.8 in the previous versions is definitely wrong.

math.AG↗

arXiv2014

Extremal transitions from nested reflexive polytopes

Using an inclusion of one reflexive polytope into another is a well-known strategy for connecting the moduli spaces of two Calabi-Yau families. In this paper we look at the question of when an inclusion of reflexive polytopes determines a torically-defined extremal transition between smooth Calabi-Yau hypersurface families. We show this is always possible for reflexive polytopes in dimensions two and three. However, in dimension four and higher, obstructions can occur. This leads to a smooth projective family of Calabi-Yau threefolds that is birational to one of Batyrev's hypersurface families, but topologically distinct from all such families.

math.AG↗