Rationality in Differential Algebraic Geometry

Abstract

Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry. Joël Merker Equivalences of 5-dimensional CR manifoldsDespite their importance, until now, the invariants of strictly pseudoconvex domains have been fully computed, to our knowledge, only in the case of the unit ball B n+1 , where they all vanish! Sidney WEBSTER ([73]).Realdenotes the standard complex structure and then T M ∩J(T M) has constant real dimension 2n =: 2 CRdimM, while dim R M = 2n+c; general C ω CR submanifolds M ⊂ C ν , i.e. those for which dim T p M ∩J(T p M) is constant for p ∈ M, are always locally CR-generic in some complex submanifold [51], hence CR-genericity is not a restriction. Problem 1. Classify local C ω CR-generic submanifolds M 2n+c ⊂ C n+c under local biholomorphisms of C n+c up to dimension 2n + c 5.an explicit Levi factor in coordinates appears:The assumption that M 3 ⊂ C 2 is smooth reads:The assumption that M is Levi nondegenerate reads:also vanishes at no point. General principle. Various geometric assumptions enter computations in denominator places. 0 ≡

On the ampleness of the cotangent bundles of complete intersections

“…whose image consists of, as a consequence of the definition (46) above, all functions f on U satisfying f (λz) = λ ♥ f (z), for all z ∈ U and for all λ ∈ K × .…”

On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci

“…identically in C{ , , }. Unfortunately, it is essentially impossible to print in a published article what one obtains after a full expansion of these two derivations; other instances of this phenomenon appear in [7,8].…”

“…[10][11][12]). Theorem 1 was presented in the Abel Symposium 2013, organized by John-Erik Fornaess, Marius Irgens, and Erlend Fornaess-Wold and announced in [7].…”

Canonical Cartan connections on maximally minimal generic submanifolds $\boldsymbol{M^5 \subset \mathbb{C}^4}$

“…A unified presentation of recent results on Cartan equivalences for all six general classes I, II, III 1 , III 2 , IV 1 , IV 2 of CR manifolds of dimension 5 is upcoming ( [3,4]).…”