scholarly journals On the variety of nets of quadrics defining twisted cubics

1981 ◽  
pp. 84-96 ◽  
Author(s):  
Geir Ellingsrud ◽  
Ragni Piene ◽  
Stein Arild Strømme
Keyword(s):  
Twisted Cubics ◽  
Nets Of Quadrics

scholarly journals A compactification of the space of twisted cubics

2002 ◽  
Vol 91 (2) ◽  
pp. 221 ◽  
Author(s):  
I. Vainsencher ◽  
F. Xavier
Keyword(s):  
Parameter Space ◽  
Ruled Surfaces ◽  
Segre Varieties ◽  
The Family ◽  
Twisted Cubics ◽  
Nets Of Quadrics ◽  
Smooth Compactification

We give an elementary, explicit smooth compactification of a parameter space for the family of twisted cubics. The construction also applies to the family of subschemes defined by determinantal nets of quadrics, e.g., cubic ruled surfaces in $\boldsymbol P^4$, Segre varieties in $\boldsymbol P^5$. It is suitable for applications of Bott's formula to a few enumerative problems.

Nets of quadrics and deformations of Σ3〈3〉 singularities

1989 ◽  
Vol 105 (1) ◽  
pp. 109-115
Author(s):  
S. A. Edwards ◽  
C. T. C. Wall
Keyword(s):  
Parameter Space ◽  
General Type ◽  
Single Parameter ◽  
Connected Components ◽  
Quadratic Maps ◽  
Nets Of Quadrics

The 2-jet of a Σ3 map-germ f:(3, 0) → (3, 0) determines a net of quadratic maps from 3 to 3; for nets of general type this jet is sufficient for equivalence. The classification of such nets involves a single parameter c. It is shown in [7], also in [3], that the versai unfolding of f is topologically trivial over the parameter space. However, there are 4 connected components of this space of nets. The main object of this paper is to show that the corresponding unfolded maps are of different topological types.

scholarly journals The Geometry of Marked Contact Engel Structures

2020 ◽  
Author(s):  
Gianni Manno ◽  
Paweł Nurowski ◽  
Katja Sagerschnig
Keyword(s):  
Local Geometry ◽  
Dimensional Manifold ◽  
Twisted Cubic ◽  
Homogeneous Models ◽  
Local Invariants ◽  
Twisted Cubics ◽  
Cubic Structure ◽  
Contact Distribution ◽  
Engel Structures ◽  
Engel Structure

AbstractA contact twisted cubic structure$$({\mathcal M},\mathcal {C},{\varvec{\upgamma }})$$ ( M , C , γ ) is a 5-dimensional manifold $${\mathcal M}$$ M together with a contact distribution $$\mathcal {C}$$ C and a bundle of twisted cubics $${\varvec{\upgamma }}\subset \mathbb {P}(\mathcal {C})$$ γ ⊂ P ( C ) compatible with the conformal symplectic form on $$\mathcal {C}$$ C . The simplest contact twisted cubic structure is referred to as the contact Engel structure; its symmetry group is the exceptional group $$\mathrm {G}_2$$ G 2 . In the present paper we equip the contact Engel structure with a smooth section $$\sigma : {\mathcal M}\rightarrow {\varvec{\upgamma }}$$ σ : M → γ , which “marks” a point in each fibre $${\varvec{\upgamma }}_x$$ γ x . We study the local geometry of the resulting structures $$({\mathcal M},\mathcal {C},{\varvec{\upgamma }}, \sigma )$$ ( M , C , γ , σ ) , which we call marked contact Engel structures. Equivalently, our study can be viewed as a study of foliations of $${\mathcal M}$$ M by curves whose tangent directions are everywhere contained in $${\varvec{\upgamma }}$$ γ . We provide a complete set of local invariants of marked contact Engel structures, we classify all homogeneous models with symmetry groups of dimension $$\ge 6$$ ≥ 6 up to local equivalence, and we prove an analogue of the classical Kerr theorem from Relativity.

II.—The Irreducible System of Concomitants of Two Double Binary (2, 1) Forms

1926 ◽  
Vol 45 (1) ◽  
pp. 3-13
Author(s):  
W. Saddler
Keyword(s):  
Quadric Surface ◽  
Binary Forms ◽  
Irreducible System ◽  
Simultaneous System ◽  
Twisted Cubics

Little is known of the details of systems of concomitants belonging to double binary forms. The cases of the single ground form of orders (1, 1), (2, 1), (2, 2) respectively, together with the simultaneous system of any number of (1, 1) forms, are the only four cases, which have been published. The following pages establish the simultaneous system of two (2, 1) forms.This system is fundamental for the geometrical treatment of two twisted cubics lying upon a quadric surface and having four common points.

scholarly journals Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects

2018 ◽  
Vol 114 ◽  
pp. 85-117 ◽  
Author(s):  
Martí Lahoz ◽  
Manfred Lehn ◽  
Emanuele Macrì ◽  
Paolo Stellari
Keyword(s):  
Moduli Space ◽  
Twisted Cubics ◽  
Cubic Fourfold

Nets of quadrics and vector bundles on a double plane

1986 ◽  
Vol 192 (1) ◽  
pp. 29-43 ◽  
Author(s):  
Usha N. Bhosle
Keyword(s):  
Vector Bundles ◽  
Double Plane ◽  
Nets Of Quadrics

scholarly journals Twisted cubics on singular cubic fourfolds—On Starr’s fibration

2017 ◽  
Vol 290 (1-2) ◽  
pp. 379-388 ◽  
Author(s):  
Christian Lehn
Keyword(s):  
Twisted Cubics

Surfaces Whose Asymptotic Curves are Twisted Cubics

1938 ◽  
Vol 60 (2) ◽  
pp. 337 ◽  
Author(s):  
E. P. Lane ◽  
M. L. MacQueen
Keyword(s):  
Asymptotic Curves ◽  
Twisted Cubics

Chords of Twisted Cubics

1923 ◽  
Vol s2-21 (1) ◽  
pp. 98-113 ◽  
Author(s):  
E. K. Wakeford
Keyword(s):  
Twisted Cubics

Surfaces with 𝐾²=𝜒=2 and special nets of quadrics in 3-space

1994 ◽  
pp. 77-128
Author(s):  
F. Catanese ◽  
P. Cragnolini ◽  
P. Oliverio
Keyword(s):  
Nets Of Quadrics
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