Roya Beheshti
Spaces of rational curves in complete intersections.
Fri, 01/21/2011 - 16:01 — SomNambulAuthors: Roya Beheshti, N. Mohan Kumar
Subjects: Algebraic Geometry
AbstractWe prove that the space of smooth rational curves of degree $e$ in a general
complete intersection of multidegree $(d_1, ..., d_m)$ in $\PP^n$ is
irreducible of the expected dimension if $\sum_{i=1}^m d_i <\frac{2n}{3}$ and
$n$ is large enough. This generalizes the results of Harris, Roth and Starr
\cite{hrs}, and is achieved by proving that the space of conics passing through
any point of a general complete intersection has constant dimension if
$\sum_{i=1}^m d_i$ is small compared to $n$.Fibers of Projections and Submodules of Deformations.
Mon, 11/23/2009 - 16:01 — SomNambulAuthors: Roya Beheshti, David Eisenbud
Subjects: Algebraic Geometry
AbstractWe bound the complexity of the fibers of the generic linear projection of a
smooth variety in terms of a new family of invariants. These invariants are
closely related to ideas of John Mather, and we give a simple proof of his
bound on the Thom-Boardman invariants of a generic projection as an
application.Non-uniruledness results for spaces of rational curves in hypersurfaces.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Roya Beheshti
Subjects: Algebraic Geometry
AbstractWe prove that the sweeping components of the space of smooth rational curves
in a smooth hypersurface of degree $d$ in $P^n$ are not uniruled if $(n+1)/2
\leq d \leq n-3$. We also show that for any positive integer $e$, the space of
smooth rational curves of degree $e$ in a general hypersurface of degree $d$ in
$P^n$ is not uniruled when $d \geq e \sqrt{n}$.
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