6 papers
Sections of Jacobian fibrations over lines
János Kollár, Giulia Saccà
Let be a linear system on a smooth surface . We study the cohomology classes of sections of the universal Jacobian over lines in . When is a K3 surface, the unive…
The Mordell-Schinzel conjecture for cubic diophantine equations
János Kollár, Jennifer Li
Building on the works of Mordell (1952) and Schinzel (2015), we prove that cubic diophantine equations have infinitely many solutions.
Essential dimension of isogenies
János Kollár, Ziquan Zhuang
We give a lower bound for the essential dimension of isogenies of complex abelian varieties. The bound is sharp in many cases. In particular, the multiplication-by- map is incom…
Flat pushforwards of Chern classes and the smoothability of cycles below the middle dimension
János Kollár, Claire Voisin
We prove in this paper the smoothability of cycles modulo rational equivalence in the Whitney range, that is, when the dimension is strictly smaller than the codimension. We introd…
Fano varieties with torsion in the third cohomology group
John Christian Ottem, Jørgen Vold Rennemo
We construct first examples of Fano varieties with torsion in their third cohomology group. The examples are constructed as double covers of linear sections of rank loci of symmetr…
Fundamental groups of rationally connected varieties
János Kollár
Let U be an open subset of a unirational variety. We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U. As a c…