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math.AG2004
The affine stratification number and the moduli space of curves
Mike Roth, Ravi Vakil
We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such that there is a stratification of X by locally closed affine…
math.AG2002
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…
math.AG2002
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…