Varieties of parity

Varieties of Competitive Parity

Strategy research explains why some firms outperform others, typically using profit rates, shareholder returns, and other continuous dependent variables. This paper investigates winning as the dependent variable, as measured by distributions of annual industry leadership in profits and returns to investors. This shift in dependent variable introduces alternative null models of competitive parit...

Modular perverse sheaves on flag varieties I: tilting and parity sheaves

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group G is a “graded version” of the category of tilting perverse sheaves on the flag variety of the dual group Ǧ, for any field of coefficients whose characteristic is good for G. We derive some consequences on Soergel’s modular category O, and on multiplicities and decomposition n...

Secant Varieties of Toric Varieties

If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...

Parity Lost and Parity Regained

RAID storage systems protect data from storage errors, such as data corruption, using a set of one or more integrity techniques, such as checksums. The exact protection offered by certain techniques or a combination of techniques is sometimes unclear. We introduce and apply a formal method of analyzing the design of data protection strategies. Specifically, we use model checking to evaluate whe...

Salt tolerance of sunflower varieties during germination