34 citations · 50 across the 5 of their papers we have counts for
8 papers
The density of rational points on non-singular hypersurfaces, II
T. D. Browning, D. R. Heath-Brown
This paper establishes the conjecture that a non-singular projective hypersurface of dimension , which is not equal to a linear space, contains rational points of h…
The Kodaira dimension of spaces of rational curves on low degree hypersurfaces
Jason Starr
For a hypersurface in complex projective space $X\subset \PP^n$, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spaces $\Kbm{0,0}{X,e}$ parametrizi…
Rational connectivity and sections of families over curves
T. Graber, J. Harris, B. Mazur +1
We show that if a family of complex varieties over a base B admits a section when restricted to a very general curve in B, then the family must contain a subfamily of rationally co…
Rational curves on hypersurfaces of low degree, II
Joe Harris, Jason Starr
This is a continuation of "Rational curves on hypersurfaces of low degree", math.AG/0203088. We prove that if d^2+d+1 < n and d > 2, then for a general hypersurface X_d in P^n of d…
A note on Hurwitz schemes of covers of a positive genus curve
Tom Graber, Joe Harris, Jason Starr
We prove the irreducibility of the space parametrizing branched covers of a fixed Riemann surface of degree , with at least 2d branch points, and with monodromy group equal…
Abel-Jacobi maps associated to smooth cubic threefolds
Joe Harris, Mike Roth, Jason Starr
We pose some questions about spaces parametrizing rational curves on rationally connected varieties. We give a partial answer for cubic threefolds. Many of our results were previou…