4 papers · 1 filter
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 $…