13 citations · 19 across the 5 of their papers we have counts for
6 papers · 1 filter
Invariant rings through categories
Jarod Alper, A. J. de Jong
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that…
Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
A. J. de Jong, Xuhua He, Jason Michael Starr
Under suitable hypotheses, we prove that a form of a projective homogeneous variety defined over the function field of a surface over an algebraically closed field has a rati…
Higher Fano manifolds and rational surfaces
A. J. de Jong, Jason Michael Starr
For a Fano manifold of pseudo-index at least 3 and nef, we show irreducibility of certain spaces of curves on the Fano manifold implies the manifold is a union of rati…
Very twisting families of pointed lines on Grassmannians
A. J. de Jong, Jason Michael Starr
There exist very twisting families of lines on Grassmannians and isotropic Grassmannians. This is a key step in proving existence of a rational section of a family of isotropic Gra…
A note on Fano manifolds whose second Chern character is positive
A. J. de Jong, Jason Michael Starr
This note outlines some first steps in the classification of Fano manifolds for which is positive or nef.
Divisor classes and the virtual canonical bundle for genus 0 maps
A. J. de Jong, Jason Michael Starr
Some divisor class relations are proved and used to compute the Cartier divisor class of the virtual canonical bundle for genus 0 maps to a smooth target.