On fourfolds with canonical curve sections

1950 ◽  
Vol 46 (3) ◽  
pp. 419-428 ◽  
Author(s):  
L. Roth
Keyword(s):  
Complete Intersections ◽  
General Character ◽  
Linear Spaces ◽  
Canonical Curve ◽  
Canonical Curves ◽  
Generic Curve

In a recent note the writer has examined the varieties whose generic curve sections are canonical curves of genus p, of general character, and whose surface sections contain only complete intersections with primals; following Fano's classification, we call these varieties of the first species. Such varieties are all rational provided that r > 3 and p > 6. In the present paper we consider their representations on linear spaces for the case r = 4, from which, in conjunction with the previous results, we conclude that fourfolds of the first species exist if, and only if, p ≤ 10; this agrees with the conjecture made by Fano in the case r = 3. It will be seen that the representation of these varieties on [4] provides interesting illustrations of Semple's formulae for composite surfaces in higher space.

scholarly journals On Fano schemes of linear spaces of general complete intersections

2020 ◽  
Vol 115 (6) ◽  
pp. 639-645
Author(s):  
Francesco Bastianelli ◽  
Ciro Ciliberto ◽  
Flaminio Flamini ◽  
Paola Supino
Keyword(s):  
Complete Intersections ◽  
Linear Spaces

CANONICAL CURVES IN ℙ3

2002 ◽  
Vol 85 (2) ◽  
pp. 333-366 ◽  
Author(s):  
JACQUELINE ROJAS ◽  
ISRAEL VAINSENCHER
Keyword(s):  
Vector Space ◽  
Hilbert Scheme ◽  
Linear Component ◽  
Arithmetic Genus ◽  
Generic Point ◽  
Rational Map ◽  
Linear Forms ◽  
Cubic Surface ◽  
Canonical Curve ◽  
Canonical Curves

Let ${\rm Hilb}^{6t-3}(\mathbb{P}^3)$ be the Hilbert scheme of closed 1-dimensional subschemes of degree 6 and arithmetic genus 4 in $\mathbb{P}^3$. Let $H$ be the component of ${\rm Hilb}^{6t-3}(\mathbb{P}^3)$ whose generic point corresponds to a canonical curve, that is, a complete intersection of a quadric and a cubic surface in $\mathbb{P}^3$. Let $F$ be the vector space of linear forms in the variables $z_1, z_2, z_3, z_4$. Denote by $F_d$ the vector space of homogeneous forms of degree $d$. Set $X = \{(f_2,f_3)\}$ where $f_2 \in \mathbb{P}(F_2)$ is a quadric surface, and $f_3 \in \mathbb{P}(F_3/f_2 \cdot F)$ is a cubic modulo $f_2$. We have a rational map, $\sigma : X \cdots \rightarrow H$ defined by $(f_2,f_3) \mapsto f_2 \cap f_3$. It fails to be regular along the locus where $f_2$ and $f_3$ acquire a common linear component. Our main result gives an explicit resolution of the indeterminacies of $\sigma$ as well as of the singularities of $H$. 2000 Mathematical Subject Classification: 14C05, 14N05, 14N10, 14N15.

scholarly journals On the number of moduli of extendable canonical curves

2002 ◽  
Vol 167 ◽  
pp. 101-115 ◽  
Author(s):  
Ciro Ciliberto ◽  
Angelo Felice Lopez
Keyword(s):  
Hyperplane Section ◽  
Large Dimension ◽  
Canonical Curve ◽  
Canonical Curves ◽  
Wahl Map ◽  
General Member

AbstractLet C ⊂ ℙg−1 be a canonical curve of genus g. In this article we study the problem of extendability of C, that is when there is a surface S ⊂ ℙg different from a cone and having C as hyperplane section. Using the work of Epema we give a bound on the number of moduli of extendable canonical curves. This for example implies that a family of large dimension of curves that are cover of another curve has general member nonextendable. Using a theorem of Wahl we prove the surjectivity of the Wahl map for the general k-gonal curve of genus g when k = 5, g ≥ 15 or k = 6, g ≥ 13 or k ≥ 7, g ≥ 12.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces
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