30 citations · 31 across the 3 of their papers we have counts for
4 papers · 1 filter
Normal differential operators and deformation theory
Paul Burchard, Herb Clemens
This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the glo…
A local proof of Petri's conjecture at the general curve
Herbert Clemens
A proof of Petri's general conjecture on the unobstructedness of linear systems on a general curve is proposed, using only the local properties of the deformation space of the pair…
Cohomology and Obstructions III: A variational form of the generalized Hodge conjecture on K-trivial threefolds
Herbert Clemens
This paper studies the Hilbert scheme of a curve on a complete-intersection K-trivial threefold, in the case in which the curve is unobstructed in the ambient variety in which the…
Counting curves which move with threefolds
Herbert Clemens, Holger P. Kley
Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstruct…