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A graph is called normal if its vertex set can be covered by cliques Q1, Q2, . . . , Qk and also by stable sets S1, S2, . . . , Sl, such that Si ∩ Qj 6= ∅ for every i, j. This notion is due to Körner, who 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,… (More)
4 Line-graphs of cubic graphs are normal 38 4.
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)
We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties; (b) this map is always finite étale; and… (More)
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.