Related papers: Transversality for Holomorphic Supercurves
In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular, interested in numerical, universal and asymptotically proper…
In this paper we study the Hilbert scheme of smooth, linearly normal, special scrolls under suitable assumptions on degree, genus and speciality.
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background…
The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are…
We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.
We prove that the derived direct image of the constant sheaf with field coefficients under any proper map with smooth source contains a canonical summand. This summand, which we call the geometric extension, only depends on the generic…
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided…
For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
This note (which makes no claim to novelty) presents a proof of the separable rational connectedness of smooth cubic hypersurfaces, in any characteristic, by showing how to explicitly construct very free curves (of degree 3) on them. -----…
This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…
We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and their singularities are of central importance in algebraic…
In this paper we study the mapping properties of the averaging operator over a variety given by a system of homogeneous equations over a finite field. We obtain optimal results on the averaging problems over two dimensional varieties whose…
Hypersurfaces of arbitrary causal character embedded in a spacetime are studied with the aim of extracting necessary and sufficient free data on the submanifold suitable for reconstructing the spacetime metric and its first derivative along…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
Let $R$ be a commutative ring with identity and $G$ a graph. An extending generalized spline on $G$ is a vertex labeling $f \in \prod_{v} M_v$, where for each edge $e=uv$ there exists an $R$-module $M_{uv}$ together with homomorphisms $…
A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module ${\cal E}$\ over a Riemannian manifold $M$.…
We study Kaehlerian manifolds with Norden metric $g$ and develop the theory of their holomorphic hypersurfaces with constant totally real sectional curvatures. We prove a classification theorem for the holomorphic hypersurfaces of…
Geometrical meaning of superstring pictures is discussed in details. An off-shell generalization of the picture changing operation and its inverse are constructed. It is demonstrated that the generalised operations are inverse to each other…
We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric…