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RESEARCH AND PUBLICATION ACTIVITIES

Numbers in [ ] refer to the list of preprints and publications


Link: Research Activities since 2000 (Click "Forschung")


A. Commutative Algebra / Algebraic Geometry


Local Cohomology

Structure of Local Cohomology Modules [22,45,48,49,54,56,64,67,70,71,74,75,93, 95,96,98,104,107]

Vanishing- and Finiteness Results [10,17,22,38,45,48,54,64,74,82,86,88,96,98,104,107]

Associated Prime Divisors of Local Cohomology Modules [48,49,52,60,62,67,6870,71,74,75]

Behaviour of Graded Components of Local Cohomology Modules [45,52,55,60,62,63,67,68,70,71,75,82,83,86,88,93, 95,98,104,107]


Cohomology of Projective Schemes

Cohomological Hilbert Functions [17,26,27,32,34,36,41,42,43,45,50,52,57,58,62,70,71,86,88, 95, 98]

Cohomological Patterns [52,55,57,71,88, 97,98]

Castelnuovo-Mumford Regularity and Related Invariants [26,27,32,35,36,42,43,45,50,52,57,58,63,76,86,88, 90, 92, 98, 99, 100]

Asymptotic Behaviour of Cohomology [52,55,57,71,75,83, 93]


Projective Varieties with Specified Numerical Invariants

Geometric Properties [46,47,53,61,72,73,85,87,89,91,94,99,101,102,103]

Secant Lines and Projections [46,54,62,73,85,87,89,91,94,99,99,101,102,103]

Cohomology [28,37,46,47,51,52,53,61,72,73,87,94,99,101,102,103]

Syzygies and Betti Numbers [53,61,72,73,87,99,101,102]

Cohomology of Ample Line Bundles [47,51,52]


Connectivity in Schemes

Local Cohomology and Connectedness Dimensions [24,25,45,98]

Asymptotic Depth and Connectivity [25,31]


Rees Rings and Macaulayfication

Affine Macaulaufication [3,4]

Local Cohomology of Rees- and Form Rings [13,19,22,23,33,35,39,45]

Macaulayfication by Blowing-up [13,18,21,34,35,39]


Specially Generated Ideals

d-Sequences [13,14,16]

Standard-Sequences [13,19,23,33,35]


Asymptotic Primes and Asymptotic Depth

Asymptotic Behaviour of Powers of Ideals [8,9,10]

Analytic Spread [9,10,16,45]

Asymptotic Behaviour of Components of Graded Modules [10,31,48,60,62]


Formal Fibres, Loci and Chains of Primes

Formal Unmixedness and Chain Conditions [1,2,5,11,20,45,56,64,98]

Properties of Formal Fibres and Loci [6,7,12,15,20,45,56,64,98]


Textbooks and Lecture Notes

Algebraic Geometry [30,45,108]

Commutative Algebra [77]

Weyl Algebras and D-Modules [100, 108]

Local Cohomology [45,51,67,75,90,92]

Elementary Number Theory [69,105,106]

Courses for Teachers [69,105,106]


B. Visualization and Popular Exposition


Visualization of Surfaces

Models of Closed Surfaces [29,41,59]

Blowing-up of Surfaces [29,40,41,44,84]


Popular Exposition

General [29,40,41,66,81]