34 citations · 50 across the 5 of their papers we have counts for
7 papers · 1 filter
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…
Curves of small degree on cubic threefolds
Joe Harris, Mike Roth, Jason Starr
We describe the Hilbert schemes parametrizing curves on a cubic threefold of degree at most 5. In a forthcoming paper, we use this description to give a new proof and extension of…