LAMA, Université Savoie Mont Blanc, Chambéry
Date(s) : 16/09/2021 iCal
14 h 00 min - 15 h 00 min
Let f be a complex polynomial with isolated singularities. In this talk, we will start by recalling classical formulas of the Euler characteristic of a fiber of f in terms of Milnor numbers of the singularities of f and the defect of equisingularity at infinity in a compactification of f. Then, we will recall the notion of motivic invariant at infinity of f coming from Denef–Loeser and Guibert–Loeser–Merle technics.
This invariant does not depend on the chosen compactification, it is generically equal to zero and, under isolated singularities assumptions, its Euler characteristic is equal to the defect of equisingularity at infinity of f for the value a. In the last part of the talk, we will consider the case of plane curves, where computations of this invariant can be done in terms of Newton polygons at infinity, using an induction process based on Newton transformations and iterated Newton polygons with decreasing height.
Joint works with Pierrette Cassou-Noguès (Bordeaux) and Lorenzo Fantini (Frankfurt).