On classes in the classification of curves on rational surfaces with respect to logarithmic plurigenera

2019 ◽  
Author(s):  
Hirotaka Ishida
Keyword(s):  
Rational Surfaces

scholarly journals Exceptional sequences of invertible sheaves on rational surfaces

2011 ◽  
Vol 147 (4) ◽  
pp. 1230-1280 ◽  
Author(s):  
Lutz Hille ◽  
Markus Perling
Keyword(s):  
Large Class ◽  
Complete Classification ◽  
Toric Surface ◽  
Structural Result ◽  
Toric Surfaces ◽  
Rational Surfaces ◽  
Exceptional Sequences

AbstractIn this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

Classification of Algebraic Surfaces with Sectional Genus less than or Equal to Six. II: Ruled Surfaces with dim ϕKx⊗L(x) = l

1986 ◽  
Vol 38 (5) ◽  
pp. 1110-1121 ◽  
Author(s):  
Elvira Laura Livorni
Keyword(s):  
Line Bundle ◽  
Hyperplane Section ◽  
Ample Line Bundle ◽  
Rational Surface ◽  
Algebraic Surfaces ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
Image Position ◽  
Smooth Hyperplane Section

Let L be a very ample line bundle on a smooth, connected, projective, ruled not rational surface X. We have considered the problem of classifying biholomorphically smooth, connected, projected, ruled, non rational surfaces X with smooth hyperplane section C such that the genus g = g(C) is less than or equal to six and dim where is the map associated to . L. Roth in [10] had given a birational classification of such surfaces. If g = 0 or 1 then X has been classified, see [8].If g = 2 ≠ hl,0(X) by [12, Lemma (2.2.2) ] it follows that X is a rational surface. Thus we can assume g ≦ 3.Since X is ruled, h2,0(X) = 0 andsee [4] and [12, p. 390].

scholarly journals Classification of algebraic non-ruled surfaces with sectional genus less than or equal to six

1985 ◽  
Vol 100 ◽  
pp. 1-9 ◽  
Author(s):  
Elvira Laura Livorni
Keyword(s):  
Line Bundle ◽  
Hyperplane Section ◽  
Ample Line Bundle ◽  
Ruled Surfaces ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
Very Ample Line Bundle ◽  
Similar Classification

In this paper we have given a biholomorphic classification of smooth, connected, protective, non-ruled surfaces X with a smooth, connected, hyperplane section C relative to L, where L is a very ample line bundle on X, such that g = g(C) = g(L) is less than or equal to six. For a similar classification of rational surfaces with the same conditions see [Li].

scholarly journals On planar Cremona maps of prime order

2004 ◽  
Vol 174 ◽  
pp. 1-28 ◽  
Author(s):  
Tommaso de Fernex
Keyword(s):  
Prime Order ◽  
Higher Dimensions ◽  
Conjugacy Classes ◽  
Geometric Constructions ◽  
Cremona Transformations ◽  
Rational Surfaces ◽  
Mori Theory ◽  
First Results

AbstractThis paper contains a new proof of the classification of prime order elements of Bir(ℙ2) up to conjugation. The first results on this topic can be traced back to classic works by Bertini and Kantor, among others. The innovation introduced by this paper consists of explicit geometric constructions of these Cremona transformations and the parameterization of their conjugacy classes. The methods employed here are inspired to [4], and rely on the reduction of the problem to classifying prime order automorphisms of rational surfaces. This classification is completed by combining equivariant Mori theory to the analysis of the action on anticanonical rings, which leads to characterize the cases that occur by explicit equations (see [28] for a different approach). Analogous constructions in higher dimensions are also discussed.

scholarly journals Birational classification of curves on rational surfaces

2010 ◽  
Vol 199 ◽  
pp. 43-93
Author(s):  
Alberto Calabri ◽  
Ciro Ciliberto
Keyword(s):  
Linear System ◽  
Plane Curve ◽  
Rational Surface ◽  
Minimal Degree ◽  
Classification Theorem ◽  
Plane Curves ◽  
Cremona Transformation ◽  
Rational Surfaces

AbstractIn this paper we consider the birational classification of pairs (S, ℒ), withSa rational surface andℒa linear system onS. We give a classification theorem for such pairs, and we determine, for each irreducible plane curveB, itsCremona minimalmodels, that is, those plane curves which are equivalent toBvia a Cremona transformation and have minimal degree under this condition.

scholarly journals Classification of rational surfaces of degree 11 and sectional genus 11 in ${\mathsf P}^{4}$

2009 ◽  
Vol 104 (1) ◽  
pp. 60 ◽  
Author(s):  
Hans-Christian Graf von Bothmer ◽  
Kristian Ranestad
Keyword(s):  
Hilbert Function ◽  
Hilbert Functions ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
The Third

We use the BGG-correspondence to show that there are at most three possible Hilbert functions for smooth rational surfaces of degree 11 and sectional genus 11. Surfaces with one of these Hilbert functions have been classified by Popescu. The classification for a second one is done in this paper. For the third Hilbert function the classification is still open.

scholarly journals Class of rational surfaces in $\mathsf P^4$

2003 ◽  
Vol 92 (2) ◽  
pp. 210
Author(s):  
Christian Voica
Keyword(s):  
A Priori ◽  
Complete Classification ◽  
Rational Surfaces

In this paper, we obtain a complete classification of all rational surfaces embedded in ${\mathsf P}^4$ so that all their exceptional curves are lines. These surfaces are exactely the rational surfaces shown by I.Bauer to project isomorphicaly from ${\mathsf P}^5$ from one of their points, although no a priori reason is known why such a surface should be projectable in this way.

scholarly journals Birational classification of curves on rational surfaces

2010 ◽  
Vol 199 ◽  
pp. 43-93 ◽  
Author(s):  
Alberto Calabri ◽  
Ciro Ciliberto
Keyword(s):  
Linear System ◽  
Plane Curve ◽  
Rational Surface ◽  
Minimal Degree ◽  
Classification Theorem ◽  
Plane Curves ◽  
Cremona Transformation ◽  
Rational Surfaces

AbstractIn this paper we consider the birational classification of pairs (S, ℒ), with S a rational surface and ℒ a linear system on S. We give a classification theorem for such pairs, and we determine, for each irreducible plane curve B, its Cremona minimal models, that is, those plane curves which are equivalent to B via a Cremona transformation and have minimal degree under this condition.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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