Markus Perling

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King's conjecture states that on every smooth complete toric variety X there exists a strongly exceptional collection which generates the bounded derived category of X and which consists of line bundles. We give a counterexample to this conjecture. This example is just the Hirzebruch surface F 2 iteratively blown up three times, and we show by explicit(More)
The compilation of RELFUN programs consists of two main stages, horizontal transformations and vertical translations. The horizontal transformer performs both source-to-source steps into a subset of RELFUN and source-to-intermediate steps into a RELFUN-like language. The vertical translator is also divided into two phases, the classiier and the code(More)
A knowledge-based process-planning system for generating workplans for idealized lathe CNC machines is discussed. It transforms CAD-like diagrams of rotational-symmetric workpieces into abstract NC programs. To simplify development and evolution , declarative representations are used for all processing stages and steps, including a qualitative simulation of(More)
This work discusses combinatorial and arithmetic aspects of cohomology vanishing for divisorial sheaves on toric varieties. We obtain a refined variant of the Kawamata-Viehweg theorem which is slightly stronger. Moreover, we prove a new vanishing theorem related to divisors whose inverse is nef and has small Iitaka dimension. Finally , we give a new(More)
We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application we consider the case of toric sheaves over toric varieties. Comparing these decompositions with primary decompositions(More)