30 citations · 31 across the 3 of their papers we have counts for
12 papers
An analogue of Abel's theorem
Herbert Clemens
This work makes a parallel construction for curves on threefolds to a ``current-theoretic'' proof of Abel's theorem giving the rational equivalence of divisors P and Q on a Riemann…
Bounding the genus of subvarieties of generic hypersurfaces from below
Herbert Clemens
A second-order invariant of C. Voisin gives a powerful method for bounding from below the geometric genus of a k-dimensional subvariety of a degree-d hypersurface in complex projec…
Cohomology and Obstructions II: Curves on K-trivial threefolds
Herbert Clemens
On a threefold with trivial canonical bundle, Kuranishi theory gives an algebro-geometry construction of the (local analytic) Hilbert scheme of curves at a smooth holomorphic curve…
On the geometric genus of subvarieties of generic hypersurfaces
Herbert Clemens, Ziv Ran
We prove some lower bounds on certain nonegative twists of the canonical bundle of a subvariety of a generic hypersurface in projective space. In particular we prove that the gener…
A Petri Theorem for Rank 2 Bundles with Canonical Determinant
Herbert Clemens, Elisa Casini
This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a ge…
On rational curves in n-space with given normal bundle
Herbert Clemens
The stable rationality of components of the moduli space of (unparametrized) rational curves in projective -space with fixed normal bundle is proved, provided these components d…