Classification of Algebraic Varieties

May 4, 2017 by Chenyang Xu

This year’s Ramanujan Prize is awarded to Chenyang Xu of Beijing International Center of Mathematical Research in China. The prize is in recognition of Xu’s outstanding works in algebraic geometry, notably in the area of birational geometry, including works both on log canonical pairs and on Q-Fano varieties, and on the topology of singularities and their dual complexes. More specifically, Xu proved in joint works with C. Hacon and J. McKernan the boundedness of log canonical pairs and resolved in the affirmative Shokurov’s ACC (Ascending Chain Condition) Conjecture on log canonical thresholds. Xu established in a joint work with C. Li a procedure by which any generically Q-Fano test configuration can be replaced by a special test configuration with Q-Fano fibers such that the Donaldson-Futaki invariant does not increase, thereby reducing K-stability issues to testing against such special test configurations. Xu proved the finiteness of algebraic fundamental groups of klt (Kawamata log terminal) singularities and in a joint work with Kollár proved for a Calabi-Yau pair (X, D) that the fundamental group of the dual complex of D is a quotient of the fundamental group of the smooth locus of X.

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