On the Hilbert scheme of curves of maximal genus in a projective space

1987 ◽  
Vol 194 (3) ◽  
pp. 351-363 ◽  
Author(s):  
Ciro Ciliberto
Keyword(s):  
Projective Space ◽  
Hilbert Scheme ◽  
Maximal Genus

The relative Hilbert scheme of projection morphisms

2016 ◽  
Vol 26 (01) ◽  
pp. 157-170
Author(s):  
Hosung Kim
Keyword(s):  
Projective Space ◽  
General Formula ◽  
Hilbert Scheme ◽  
Weighted Projective Space ◽  
Line Bundles ◽  
Smooth Hypersurface

Let [Formula: see text] be a smooth hypersurface of degree [Formula: see text] in a projective space [Formula: see text] and take a point [Formula: see text] in [Formula: see text]. Let [Formula: see text] be the relative Hilbert scheme parametrizing zero-dimensional subscheme, of length [Formula: see text], of fibers of the projection morphism [Formula: see text] from [Formula: see text]. In this paper we present an embedding of the relative Hilbert scheme [Formula: see text] into a weighted projective space and describe its defining ideal for general [Formula: see text]. We also study line bundles on the relative Hilbert scheme [Formula: see text] for [Formula: see text] and general [Formula: see text].

scholarly journals The degree of the tangent and secant variety to a projective surface

2020 ◽  
Vol 20 (2) ◽  
pp. 233-248
Author(s):  
Andrea Cattaneo
Keyword(s):  
Projective Space ◽  
Hilbert Scheme ◽  
Projective Surface ◽  
Secant Variety ◽  
Smooth Projective Surface

AbstractWe present a way of computing the degree of the secant (resp. tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is 3-very ample. This method exploits the link between these varieties and the Hilbert scheme 0-dimensional subschemes of length 2 of the surface.

scholarly journals Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Andrew J. McLeod ◽  
Cristian Vergu ◽  
Matthias Volk ◽  
Matt von Hippel ◽  
...  
Keyword(s):  
Projective Space ◽  
Feynman Integral ◽  
Weighted Projective Space

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

scholarly journals Transverse Hilbert schemes and completely integrable systems

2017 ◽  
Vol 4 (1) ◽  
pp. 263-272 ◽  
Author(s):  
Niccolò Lora Lamia Donin
Keyword(s):  
Integrable Systems ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Initial Surface ◽  
Hilbert Schemes ◽  
Completely Integrable Systems ◽  
Completely Integrable ◽  
Symplectic Surface ◽  
Complex Symplectic ◽  
Minimum Polynomial

Abstract In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

scholarly journals Varieties of minimal rational tangents on double covers of projective space

2012 ◽  
Vol 275 (1-2) ◽  
pp. 109-125 ◽  
Author(s):  
Jun-Muk Hwang ◽  
Hosung Kim
Keyword(s):  
Projective Space ◽  
Double Covers

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Sign in / Sign up

Export Citation Format

Share Document