J'anos Koll'ar

activity

20232026

collaborators

4 papers

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 $F_{2}$ whose only singularity is a double point

János Kollár

We exhibit planar, rational curves of large degree over $F_{2}$ that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for…

math.AG2025

Néron models, minimal models, and birational group actions

János Kollár

Let $A_{K}$ be an Abelian variety over the quotient field of a Dedekind domain $R$ . We show that the identity component of the Néron model of $A_{K}$ acts regularly on any minimal mode…

math.AG2023

Comments on Fano varieties with torsion in $H^{3} (X, Z)$ by J. C. Ottem and J. V. Rennemo

János Kollár

Ottem and Rennemo constructed a Fano 4-fold with torsion in $H_{2} (X, Z)$ . We simplify the computation of $H_{2} (X, Z)$ and also exhibit 2 lines $L^{'}, L^{''} \subset X$ such…

Theorems of Bertini and Chevalley

Planar, rational curves over F2​ whose only singularity is a double point

Néron models, minimal models, and birational group actions

Comments on Fano varieties with torsion in H3(X,Z) by J. C. Ottem and J. V. Rennemo

Planar, rational curves over $F_{2}$ whose only singularity is a double point

Comments on Fano varieties with torsion in $H^{3} (X, Z)$ by J. C. Ottem and J. V. Rennemo