10 citations · 20 across the 10 of their papers we have counts for
11 papers
Quadratic points on double planes
Nathan Chen, Ben Church, Hector Pasten +1
Zariski dense collections of quadratic points on curves are well-understood by results of Harris--Silverman and Vojta, but when there is not an analogous geomet…
The fibering genus of Fano hypersurfaces
Nathan Chen, Benjamin Church, Lena Ji +1
Kollár proved that a very general -dimensional complex hypersurface of degree at least is not birational to a fibration in rational curves. This is most…
Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties
Nathan Chen, Benjamin Church, Feng Hao
A result of Popa and Schnell shows that any holomorphic 1-form on a smooth complex projective variety of general type admits zeros. More generally, given a variety which admits…
Fano hypersurfaces with no finite order birational automorphisms
Nathan Chen, Lena Ji, David Stapleton
We use the specialization homomorphism for the birational automorphism group to study finite order birational automorphisms. For a family of varieties over a DVR, we prove that a b…
Rational maps from products of curves to surfaces with
Nathan Chen, Olivier Martin
We study dominant rational maps from a product of two curves to surfaces with . Given two curves which satisfy a mild genericity assumption and have large genus rela…
Multiplicative bounds for measures of irrationality on complete intersections
Nathan Chen
We show that measures of irrationality on very general codimension two complete intersections and very general complete intersection surfaces are multiplicative in the degrees of t…
Higher index Fano varieties with finitely many birational automorphisms
David Stapleton, Nathan Chen
Determining when the birational automorphism group of a Fano variety is finite is an interesting and difficult problem. The main technique for studying this problem is by the Noeth…
Rational endomorphisms of Fano hypersurfaces
Nathan Chen, David Stapleton
We show that the degrees of rational endomorphisms of very general complex Fano and Calabi-Yau hypersurfaces satisfy certain congruence conditions by specializing to characteristic…
Nodal elliptic curves on K3 surfaces
Nathan Chen, François Greer, Ruijie Yang
Let be a general primitively polarized K3 surface with for some integer . The Severi variety is defined to be the locus of…
Fano hypersurfaces with arbitrarily large degrees of irrationality
Nathan Chen, David Stapleton
We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index e, then the degree of irrationality of a very ge…
Degree of irrationality of very general abelian surfaces
Nathan Chen
The degree of irrationality of a projective variety is defined to be the smallest degree rational dominant map to a projective space of the same dimension. For abelian surfaces…