arXiv subjects
Publications and source records attributed to Anna Bot.
We show that a ring closely related to the Grothendieck ring of varieties has nilpotent elements, provided that the characteristic of the ground field is equal to $11$ or at least $17$.
We show that the ordinal of the dynamical degrees of all complex birational maps of the projective plane is $\omega^\omega$.
We propose a framework to give a precise meaning to the intuitive notion of "family of real forms of a variety parametrised by a variety" and study some fundamental properties of this notion. As an illustration, for any $n \geq 1$, we construct the first example of a quasi-projective real surface whose mutually non-isomorphic real forms admit a moduli of dimension at least $n$, parametrised by the real points of an affine $n$-space. Expanding on these constructions, we can give quasi-projective real varieties of any dimension whose algebraic moduli of the non-isomorphic real forms has arbitrarily positive dimension.
We describe the real forms of Gizatullin surfaces of the form $xy=p(z)$ and of Koras-Russell threefolds of the first kind. The former admit zero, two, three, four or six isomorphism classes of real forms, depending on the degree and the symmetries of the polynomial~$p$. The latter, which are threefolds given by an equation of the form $x^dy+z^k+x+t^\ell=0$, all admit exactly one real form up to isomorphism.
We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.