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Some New Results on Rationality (Lecture - 01) by Claire Voisin

1,326 views · Published 3 October 2018 · 1:17:19 · Indexed 23 September 2026

Channel: International Centre for Theoretical Sciences · 2018 · Science & Technology

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Infosys-ICTS Ramanujan Lectures: Some New Results on Rationality

Speaker: Claire Voisin (College de France)
Date:  01 October 2018, 16:00 to 5 October 2018, 10:30 AM
Venue: Madhava Lecture Hall, ICTS Campus

Lecture 1: Some new results on rationality

Date & Time: Monday, 1 October 2018, 04:00 PM

Abstract: An algebraic variety is rational if it is birational to the projective space or affine space of the same dimension. In dimension 1 and 2 and over the complex numbers, smooth projective rational varieties have several characterizations and in particular it is known that they are the same as unirational or rationally connected varieties. Starting from dimension 3, it has been proved in the 70's that there are varieties which are unirational (that is rationally dominated by projective space) but not rational. I will describe in this talk further obstructions to rationality, which have been proved recently to be very effective and powerful, as a consequence of the degeneration argument that I introduced. The key notion is that of decomposition of the diagonal in the spirit of Bloch and Srinivas.

Chow groups and birational invariants:

Lecture 2: Obstructions to rationality: unramified cohomology
Date & Time: Tuesday, 2 October 2018, 10:30 AM 

Lecture 3: Zero-cycles and decomposition of the diagonal
Date & Time: Wednesday, 3 October 2018, 10:30 AM 

Lecture 4: The degeneration method and various  improvements
Date & Time:  Thursday, 4 October 2018, 10:30 AM 

Lecture 5: Cohomological decomposition of the diagonal in small dimension.
Date & Time: Friday, 5 October 2018, 10:30 AM
 
This lecture is part of the discussion meeting Complex Algebraic Geometry.

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