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math.AG2026
Theorems of Bertini and Chevalley
János Kollár
We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreduci…
math.AG2026
Planar, rational curves over whose only singularity is a double point
János Kollár
We exhibit planar, rational curves of large degree over that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for…