Seminars

The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123

Events in September 2023–February 2024

  • - Hamid Hassanzadeh (Mathematics Institute, Federal University of Rio de Janeiro) -- An Algebraic Study of Bir(X)
    Hamid Hassanzadeh (Mathematics Institute, Federal University of Rio de Janeiro) -- An Algebraic Study of Bir(X)

    Category: General Hamid Hassanzadeh (Mathematics Institute, Federal University of Rio de Janeiro) -- An Algebraic Study of Bir(X)

    10h30-11h30
    18 September 2023

    Let X be a projective variety. In this talk, we explain some of the difficulties of studying the group of birational maps over X  in comparison with those over \mathbb{P}^n.
    We define the concept of birational maps of clear polynomial degree d over an arbitrary projective variety.
    We show how to replace classical techniques such as the Jacobian criterion with commutative algebraic counterparts such as analytic spread  and Hilbert functions that provide facilities to study Bir(X) in full generality.
    We show that the loci of ideals in the principal class, ideals of grade at least two, and ideals of maximal analytic spread are Zariski open sets in the parameter space.
    As an application, we show that the set of birational maps of  clear polynomial degree d over an arbitrary projective variety X, denoted by Bir(X)_{d}, is a constructible set.
    This extends a previous result by Blanc and Furter.
    Salle Byron Blanc (Y106), Inria

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