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The main theme of this thesis is the interplay between algebraic and tropical intersection
theory, especially in the context of enumerative geometry. We begin by exploiting
well-known results about tropicalizations of subvarieties of algebraic tori to give a
simple proof of Nishinou and Siebert’s correspondence theorem for rational curves
through given points in toric varieties. Afterwards, we extend this correspondence
by additionally allowing intersections with psi-classes. We do this by constructing
a tropicalization map for cycle classes on toroidal embeddings. It maps algebraic
cycle classes to elements of the Chow group of the cone complex of the toroidal
embedding, that is to weighted polyhedral complexes, which are balanced with respect
to an appropriate map to a vector space, modulo a naturally defined equivalence relation.
We then show that tropicalization respects basic intersection-theoretic operations like
intersections with boundary divisors and apply this to the appropriate moduli spaces
to obtain our correspondence theorem.
Trying to apply similar methods in higher genera inevitably confronts us with moduli
spaces which are not toroidal. This motivates the last part of this thesis, where we
construct tropicalizations of cycles on fine logarithmic schemes. The logarithmic point of
view also motivates our interpretation of tropical intersection theory as the dualization
of the intersection theory of Kato fans. This duality gives a new perspective on the
tropicalization map; namely, as the dualization of a pull-back via the characteristic
morphism of a logarithmic scheme.
Enantiomerically pure, C2-symmetric 2,6-bis(pyrazol-3-yl) pyridine ligands were obtained by treatment of diethyl-2,6-pyridinedicarbonate with (1R,4R)-(+)-camphor in the presence of NaH followed by ring closure with hydrazine. After twofold N-alkylation at the pyrazole rings, the addition of iron(II) chloride led to the according pentacoordinate dichloridoiron(II) complexes. All intermediates of the ligand synthesis, the ligands bearing NCH3 and NCH2C6H5 groups and the derived iron(II) complexes were structurally characterized by means of X-ray structure analysis. In-situ reaction with iron(II) carboxylates resulted in the formation of iron(II) carboxylate complexes, which turned out to be highly active in the hydrosilylation of acetophenone. However, even at room temperature, the enantiomeric excess of the product 1-phenylethanol is poor. 57Fe Mössbauer spectroscopy gave an insight into the species formed during catalysis.