Speaker : Professor Changho Keem (Seoul National University)
Title : Hilbert scheme of smooth projective algebraic curves
Time : 2018-12-20 (Thu) 15:00 - 16:00
Place : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: Very often in algebraic geometry, the totality of geometric objects under some natural setting becomes again an algebraic variety, which is one the main object of study in algebraic geometry.
Hilbert scheme is one of such space parametrizing families of projective algebraic varieties having the same fixed Hilbert polynomial, i.e. sharing certain basic extrinsic attributes and intrinsic invariants.
In this talk we will start with the very basic and easy construction of the Hilbert scheme of projective algebraic curves due to Alexander Grothendiek.
We then proceed to discuss about the current state of affairs especially on the irreducibility and rigidity of the Hilbert scheme after reviewing a brief history of the study since the era of Italian school.