Irreversible odd degree curves in RP2

par Kişisel Özgür

vendredi 20 sept. 2024, 11:15 → 12:15 Europe/Paris

112 (ICJ)

A smooth hypersurface $X\subset {\mathbb{RP}}^{n+1}$ of degree
$d$ is called reversible if its defining homogeneous polynomial $f$
can be continuously deformed to $-f$ without creating singularities
during the deformation. The question of reversibility was discussed in
the paper titled ``On the deformation chirality of real cubic
fourfolds'' by Finashin and Kharlamov. For $n=1$, the case of plane
curves, and $d\le 5$ odd, it is known that all smooth curves of
degree $d$ are reversible. Our goal in this talk is to present an obstruction for reversibility of odd degree curves and use it in particular to demonstrate that 
there exist irreversible curves in $  \mathbb{RP}^2 ^$$$$$$$$$$$  ^$$$ $forallodddegrees$d\geq 7$. This talk is based on joint work in progress with Ferit
Öztürk.