Rational surfaces with finitely generated Cox rings and very high Picard numbers

2016 ◽  
Vol 111 (2) ◽  
pp. 297-306 ◽  
Author(s):  
Brenda Leticia De La Rosa-Navarro ◽  
Juan Bosco Frías-Medina ◽  
Mustapha Lahyane
Keyword(s):  
Finitely Generated ◽  
Rational Surfaces ◽  
Cox Rings ◽  
Very High

scholarly journals Gorensteinness and iteration of Cox rings for Fano type varieties

2022 ◽  
Author(s):  
Lukas Braun
Keyword(s):  
Class Group ◽  
Reductive Group ◽  
Finitely Generated ◽  
Projective Varieties ◽  
Cox Rings ◽  
Cox Ring

AbstractWe show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of Fano type and Kawamata log terminal quasicones X, iteration of Cox rings is finite with factorial master Cox ring. In particular, even if the class group has torsion, we can express such X as quotients of a factorial canonical quasicone by a solvable reductive group.

Harbourne–Hirschowitz surfaces whose anticanonical divisors consist only of three irreducible components

2018 ◽  
Vol 29 (12) ◽  
pp. 1850072 ◽  
Author(s):  
J. B. Frías-Medina ◽  
M. Lahyane
Keyword(s):  
Rational Curves ◽  
Finitely Generated ◽  
Generating Sets ◽  
Cox Rings ◽  
Irreducible Components

In this paper, we provide new families of Harbourne–Hirschowitz surfaces whose effective monoids are finitely generated, and consequently, their Cox rings are finitely generated. Indeed, these properties are achieved by imposing some reasonable numerical conditions. Our method gives an efficient way of computing the minimal generating sets whenever the effective monoids are finitely generated. These surfaces are anticanonical ones having triangle anticanonical divisors consisting of smooth projective rational curves. Moreover, we present some families that do not satisfy the imposed numerical conditions but their effective monoids are still finitely generated by giving explicitly the minimal generating sets.

scholarly journals Examples of Non-finitely Generated Cox Rings

2019 ◽  
Vol 62 (02) ◽  
pp. 267-285
Author(s):  
José Luis González ◽  
Kalle Karu
Keyword(s):  
Toric Varieties ◽  
Higher Dimension ◽  
Picard Number ◽  
Finitely Generated ◽  
Toric Surfaces ◽  
Cox Rings

AbstractWe bring examples of toric varieties blown up at a point in the torus that do not have finitely generated Cox rings. These examples are generalizations of our earlier work, where toric surfaces of Picard number 1 were studied. In this article we consider toric varieties of higher Picard number and higher dimension. In particular, we bring examples of weighted projective 3-spaces blown up at a point that do not have finitely generated Cox rings.

scholarly journals Cox rings of rational surfaces and redundant blow-ups

2015 ◽  
Vol 368 (11) ◽  
pp. 7727-7743 ◽  
Author(s):  
DongSeon Hwang ◽  
Jinhyung Park
Keyword(s):  
Rational Surfaces ◽  
Cox Rings

scholarly journals Cox rings of rational surfaces and flag varieties of ADE-types

2015 ◽  
Vol 23 (2) ◽  
pp. 293-317 ◽  
Author(s):  
Naichung Conan Leung ◽  
Jiajin Zhang
Keyword(s):  
Flag Varieties ◽  
Rational Surfaces ◽  
Cox Rings

scholarly journals On Cox rings of K3 surfaces

2010 ◽  
Vol 146 (4) ◽  
pp. 964-998 ◽  
Author(s):  
Michela Artebani ◽  
Jürgen Hausen ◽  
Antonio Laface
Keyword(s):  
K3 Surfaces ◽  
Del Pezzo Surfaces ◽  
K3 Surface ◽  
Picard Number ◽  
Finitely Generated ◽  
Generators And Relations ◽  
Cox Rings ◽  
Double Covers ◽  
Del Pezzo ◽  
Effective Cone

AbstractWe study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

scholarly journals Some non-finitely generated Cox rings

2015 ◽  
Vol 152 (5) ◽  
pp. 984-996 ◽  
Author(s):  
José Luis González ◽  
Kalle Karu
Keyword(s):  
Moduli Space ◽  
Smooth Point ◽  
Large Family ◽  
Projective Planes ◽  
Finitely Generated ◽  
Genus Zero ◽  
Cox Rings ◽  
Cox Ring

We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space$\overline{M}_{0,n}$of stable$n$-pointed genus-zero curves does not have a finitely generated Cox ring if$n$is at least$13$.

Very High Resolution Analysis of the Dynamics of a Coronal Plasmoid

1994 ◽  
Vol 144 ◽  
pp. 593-596
Author(s):  
O. Bouchard ◽  
S. Koutchmy ◽  
L. November ◽  
J.-C. Vial ◽  
J. B. Zirker
Keyword(s):  
High Resolution ◽  
Solar Eclipse ◽  
Total Solar Eclipse ◽  
Field Of View ◽  
Small Field ◽  
High Resolution Analysis ◽  
Ccd Observations ◽  
Resolution Analysis ◽  
Very High ◽  
Small Field Of View

AbstractWe present the results of the analysis of a movie taken over a small field of view in the intermediate corona at a spatial resolution of 0.5“, a temporal resolution of 1 s and a spectral passband of 7 nm. These CCD observations were made at the prime focus of the 3.6 m aperture CFHT telescope during the 1991 total solar eclipse.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Decomposition of the metastable beta titanium alloy Ti-15-3

1983 ◽  
Vol 41 ◽  
pp. 264-265
Author(s):  
Y. L. Chen ◽  
S. Fujlshiro
Keyword(s):  
Low Cost ◽  
High Strength ◽  
Alpha Phase ◽  
Thick Sheet ◽  
Omega Phase ◽  
Beta Titanium Alloy ◽  
Beta Titanium ◽  
Beta Matrix ◽  
Metastable Beta ◽  
Very High

Metastable beta titanium alloys have been known to have numerous advantages such as cold formability, high strength, good fracture resistance, deep hardenability, and cost effectiveness. Very high strength is obtainable by precipitation of the hexagonal alpha phase in a bcc beta matrix in these alloys. Precipitation hardening in the metastable beta alloys may also result from the formation of transition phases such as omega phase. Ti-15-3 (Ti-15V- 3Cr-3Al-3Sn) has been developed recently by TIMET and USAF for low cost sheet metal applications. The purpose of the present study was to examine the aging characteristics in this alloy.The composition of the as-received material is: 14.7 V, 3.14 Cr, 3.05 Al, 2.26 Sn, and 0.145 Fe. The beta transus temperature as determined by optical metallographic method was about 770°C. Specimen coupons were prepared from a mill-annealed 1.2 mm thick sheet, and solution treated at 827°C for 2 hr in argon, then water quenched. Aging was also done in argon at temperatures ranging from 316 to 616°C for various times.

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