Forschung

Projective Varieties of Maximal Sectional Regularity

Research and Publishing Activities since 2000

Primary: Commutative Algebra and its Interaction with Algebraic Geometry

Local Cohomology

• Structure of Local Cohomology Modules

• Vanishing- and Finiteness Results

• Associated Primes of Local Cohomology Modules

• Behaviour of Graded Components

Cohomology of Projective Schemes

• Cohomological Hilbert Functions

• Cohomological Patterns

• Castelnuovo-Regularity and Related Invariants

Projective Varieties of low Degree

• Geometric Characterizations

• Cohomology and Hartshorne-Rao Functions

• Approximation of Betti-Numbers

• Cohomology of Ample Line Bundles

Projective Varieties of Maximal Sectional Regularity

• Geometry and Projecting Scrolls

• Extremal Secant Lines and Extremal Secant Varieties

• Cohomological Properties and Betti Numbers

• The Case of Codimension 2

• Classification

Secondary: Visualization and Popular Exposition of Mathematics

Visualization of Surfaces

• Models of closed Surfaces

• Paremetrization and Physical Realization

Blowups of the Real Affine Plane

• Embedded Blowups with respect to a Pair of Polynomials

• Embedded Isomorphisms and Isotopic Families

• Animated Visualization