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A graph is called normal if its vertex set can be covered by cliques introduced the class of normal graphs as an extension of the class of perfect graphs. Normality has also relevance in information theory. Here we prove, that the line graphs of cubic graphs are normal.

- CHRISTOPHER D. HACON, ZSOLT PATAKFALVI
- 2014

We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the Albanese map when the Frobenius stable Kodaira dimension is zero.

- Christopher Hacon, Zsolt Patakfalvi
- 2016

We show that if X is a smooth projective variety over an algebraically closed field of characteristic p > 0 such that κ(X) = 0 and the Albanese morphism is generically finite with degree not divisible by p, then X is birational to an abelian variety. We also treat the cases when a is separable (possibly with degree divisible by p) and A is either… (More)

4 Line-graphs of cubic graphs are normal 38 4.

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