Guide Classification of Algebraic Varieties

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Their goal is to cover some active topics in algebraic geometry: homological methods, discrete and arithmetic aspects, and singularitiesFaculty of Mathematics and Computer Science, University of Bucharest A special feature of this event will be a close relation to the George Enescu Music Festival.

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Homological methods Syzygies of a projective variety are very fine numerical invariants that control the embedding of the variety. From the syzygies, one can easily recover the Hilbert function, however, their outmost importance comes from the fact that they carry intrinsic geometric properties. They can be used to extract information on the geometry of moduli spaces of polarized varieties.

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Discrete aspects They originate in the theory of toric varieties linking algebraic varieties to convex geometry and combinatorics. Nowadays, the field has expanded into several directions like tropical geometry, Berkovich-spaces, and Newton-Okounkov bodies.

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Algebro-geometric theories like the minimal model program have counterparts in discrete geometry. Singularities Singularity theory is essential in the classification of algebraic varieties. While the classification in dimension one and two can be done in the smooth setting, from dimension three on the minimal model program heavily relies on singular varieties.

On the classification of algebraic varieties

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Apparel or Gift: false. Online Price 1 Label: List. The proposed participants and observers have been selected for their past contributions and current activity in the field and the meeting can be expected to produce concrete plans for future cooperation and exchange. Therefore, this proposal fulfills the objectives of the Program in its exchange and transfer of scientific knowledge through an international collaboration. Please report errors in award information by writing to: awardsearch nsf.

Classification of Algebraic Varieties

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