Lüroth’s theorem (Lüroth 1876 for \(k = \mathbb{C}\), Steinitz 1910 in general). If \(k \subseteq K\) are fields such that \(k \subseteq K \subseteq k(x)\), where \(x\) is an indeterminate over \(k\), then \(K = k(g)\) for some rational function \(g\) of \(x\) over \(k\). I am going to present a “constructive” proof of Lüroth’s… Continue reading Lüroth’s theorem (a “constructive” proof)
Month: December 2021
Publications
Overview Starting from my PhD thesis Towards a Bezout-type Theory of Affine Varieties written at University of Toronto under the supervision of Pierre Milman, my research in math falls under two broad themes: I am in particular interested in one of the simplest cases of the first problem: Book How many zeroes? Papers Compactification of… Continue reading Publications
Simplest singularity on non-algebraic normal Moishezon surfaces
A classical question in complex analytic geometry is to understand when a given analytic space is algebraic (i.e. analytification of an algebraic scheme). A necessary condition for this to hold is that the transcendence degree of the field of global meromorphic functions must be equal to the dimension of the space, i.e. the space has… Continue reading Simplest singularity on non-algebraic normal Moishezon surfaces