Research Interests - Classical Algebraic Geometry
The following paper got me interested in coding theory:
A sextic surface cannot
have 66 nodes, Journal of Algebraic Geometry 6 (1997), 151-168.
(See erratum.)
In connection with this, please have a look at Stephan
Endraß' beautiful
movie
of Barth's example of a sextic surface having 65 nodes.
My major area of interest in algebraic geometry before that was the problem
of set-theoretic complete intersections in P3.
Applications of iterated curve blowup to set theoretic complete
intersections in P3, Journal fur die reine und angewandte Mathematik
464 (1995), 1-45.
Smooth curves on a cone which pass through its
vertex, Manuscripta Math. 73 (1991), 187-205
On set theoretic complete intersection in P3
, Math. Annalen 285 (1989), 165-176.
Space curves which are the intersection of a cone
with another surface, Duke Math. J. 57 (1988), 859-876.
my Phd thesis (1987).
For results on how curves can pass through singular points on
surfaces, see:
Local geometry of smooth curves passing through
rational double points, Math. Annalen 294 (1992), 645-660.
One more paper:
On Kodaira vanishing for singular varieties, Proceedings of the
AMS 105 (1989), 911-916. (Joint with Donu Arapura.)
Reprints of all these articles are available from
me by slow mail.