6 papers
Stability of normal bundles of Brill--Noether curves in
Izzet Coskun, Eric Jovinelly, Eric Larson
We prove that a general Brill--Noether curve of genus and degree in has stable normal bundle if and only if $$(g, d) \notin \{(2,6), (3,7),…
Stability of natural bundles on curves
Izzet Coskun, Eric Larson, Isabel Vogt
In this paper, we survey recent developments concerning the stability of naturally defined bundles on curves that play a central role in the deformation theory of the curve.
The interpolation problem: When can you pass a curve of a given type through N random points in space?
Eric Larson, Ravi Vakil, Isabel Vogt
The interpolation problem is a natural and fundamental question whose roots trace back to ancient Greece. The story is long and rich, with many chapters, and a complete solution ha…
Normal bundles of rational curves in Grassmannians
Izzet Coskun, Eric Larson, Isabel Vogt
In projective space over fields of characteristic different from 2, the normal bundle of a general nondegenerate rational curve is balanced. The corresponding statement for rationa…
Generic Beauville's Conjecture
Izzet Coskun, Eric Larson, Isabel Vogt
Let be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under is semistable if the genus of is at least $…
Interpolation for Brill--Noether curves
Eric Larson, Isabel Vogt
In this paper we determine the number of general points through which a Brill--Noether curve of fixed degree and genus in any projective space can be passed.