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J. Hausen Mathematisches Institut, UniversitЁ Tuebingen at Tuebingen, Germany juergen.hausen@uni-tuebingen.de

Cox rings and Combinatorics
Generalizing a construction of D. Cox for toric varieties, one may associate to any variety X with finitely generated free divisor class group K := Cl(X ) a K -graded homogeneous coordinate ring, its "Cox ring" R(X ). We show that geometrical properties X can be described by suitable combinatorial data in X . We discuss applications to GIT and embeddings of homogeneous spaces.

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