Add to ORKGAbstract. For a general hypersurface of degree d in projective n-space, if n ≥ d2 the spaces of 2-pointed rational curves on the hypersurface are rationally connected; thus the hypersurfaces are rationally simply connected. This paper proves stronger versions of theorems in [HS05]. 1
Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “suffi...
Every rationally connected variety over the function field of a curve has a rational poin
There has been recent progress in the question of which unirational hypersurfaces are rational. Clas...
Survey paper on the theme of rationality and uniratioality in Algebraic Geometry. The contents foll...
Abstract. By studying the theory of rational curves, we introduce a notion of rational simple connec...
We study rational surfaces on very general Fano hypersurfaces in $\mathbb{P}^n$, with an eye toward ...
Abstract. We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurf...
We investigate the dimensions of the spaces of rational curves on hypersurfaces, and various related...
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools f...
Abstract. We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurf...
In the 1950s Lang studied the properties of $C_1$ fields, that is, fields over which every hypersurf...
In the 1950s Lang studied the properties of $C_1$ fields, that is, fields over which every hypersurf...
Long version (50 pages)Quasi algebraically closed fields, or $C_1$ fields, are defined in terms of a...
We study various measures of irrationality for hypersurfaces of large degree in projective space and...
We study various measures of irrationality for hypersurfaces of large degree in projective space and...
Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “suffi...
Every rationally connected variety over the function field of a curve has a rational poin
There has been recent progress in the question of which unirational hypersurfaces are rational. Clas...
Survey paper on the theme of rationality and uniratioality in Algebraic Geometry. The contents foll...
Abstract. By studying the theory of rational curves, we introduce a notion of rational simple connec...
We study rational surfaces on very general Fano hypersurfaces in $\mathbb{P}^n$, with an eye toward ...
Abstract. We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurf...
We investigate the dimensions of the spaces of rational curves on hypersurfaces, and various related...
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools f...
Abstract. We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurf...
In the 1950s Lang studied the properties of $C_1$ fields, that is, fields over which every hypersurf...
In the 1950s Lang studied the properties of $C_1$ fields, that is, fields over which every hypersurf...
Long version (50 pages)Quasi algebraically closed fields, or $C_1$ fields, are defined in terms of a...
We study various measures of irrationality for hypersurfaces of large degree in projective space and...
We study various measures of irrationality for hypersurfaces of large degree in projective space and...
Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “suffi...
Every rationally connected variety over the function field of a curve has a rational poin
There has been recent progress in the question of which unirational hypersurfaces are rational. Clas...