Generically Trivial Azumaya Algebras on a Rational Surface with a Non Rational Singularity

2013 ◽  
Vol 41 (11) ◽  
pp. 4333-4338
Author(s):  
Djordje N. Bulj ◽  
Timothy J. Ford ◽  
Drake M. Harmon
Keyword(s):  
Rational Surface ◽  
Rational Singularity ◽  
Azumaya Algebras

scholarly journals Frobenius categories, Gorenstein algebras and rational surface singularities

2014 ◽  
Vol 151 (3) ◽  
pp. 502-534 ◽  
Author(s):  
Martin Kalck ◽  
Osamu Iyama ◽  
Michael Wemyss ◽  
Dong Yang
Keyword(s):  
Sufficient Conditions ◽  
Rational Surface ◽  
Gorenstein Ring ◽  
Projective Modules ◽  
Rational Singularity ◽  
Gorenstein Projective Modules ◽  
Surface Singularities ◽  
Frobenius Category ◽  
Rational Surface Singularity ◽  
Frobenius Categories

AbstractWe give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga–Gorenstein ring. We then apply this result to the Frobenius category of special Cohen–Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga–Gorenstein rings of finite Gorenstein projective type. We also apply our method to representation theory, obtaining Auslander–Solberg and Kong type results.

RELATIONS BETWEEN MULTIPLICITY AND DIVISOR CLASS GROUP FOR RATIONAL SURFACE SINGULARITIES

2010 ◽  
Vol 21 (07) ◽  
pp. 915-938
Author(s):  
R. V. GURJAR ◽  
VINAY WAGH
Keyword(s):  
Quadratic Forms ◽  
Class Group ◽  
Rational Surface ◽  
Positive Definite ◽  
Rational Singularity ◽  
Divisor Class Group ◽  
Divisor Class ◽  
Rational Double Point ◽  
Surface Singularities ◽  
Rational Surface Singularity

In this paper we prove that a rational surface singularity with divisor class group ℤ/(2) is a rational double point. This generalizes a result by Brieskorn: if the divisor class group of a rational singularity is trivial then it is the E8 singularity [3]. We also prove several inequalities involving the integers e, δ, mi, [Formula: see text], where [Formula: see text] is the fundamental cycle. The proof of this result uses ideas from Minkowski's theory of reduction of positive-definite quadratic forms. We also give some interesting counterexamples to some of the related questions in this context.

Rational Surface Engineering of MXene@N-doping Hollow Carbon Dual-confined Cobalt Sulfides/Selenides for Advanced Aluminum Batteries

2021 ◽  
Author(s):  
Long Yao ◽  
Shunlong Ju ◽  
Xuebin Yu
Keyword(s):  
Surface Engineering ◽  
Rational Surface ◽  
Natural Abundance ◽  
Multivalent Ions ◽  
N Doping ◽  
Hollow Carbon

Rechargeable aluminum batteries (RABs) based on multivalent ions transfer have attracted great attention due to their large specific capacities, natural abundance, and high safety of metallic Al anode. However, the...

Double cover K3 surfaces of Hirzebruch surfaces

2021 ◽  
Vol 21 (2) ◽  
pp. 221-225
Author(s):  
Taro Hayashi
Keyword(s):  
Rational Surface ◽  
K3 Surfaces ◽  
Double Cover ◽  
Double Covering ◽  
Smooth Surfaces ◽  
Branch Locus ◽  
Hirzebruch Surfaces ◽  
Double Covers

Abstract General K3 surfaces obtained as double covers of the n-th Hirzebruch surfaces with n = 0, 1, 4 are not double covers of other smooth surfaces. We give a criterion for such a K3 surface to be a double covering of another smooth rational surface based on the branch locus of double covers and fibre spaces of Hirzebruch surfaces.

scholarly journals The resolution property via Azumaya algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Siddharth Mathur
Keyword(s):  
Azumaya Algebras ◽  
Algebraic Space ◽  
Local Methods ◽  
Artin Stacks ◽  
Resolution Property

Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras. Our construction passes through the case of tame Artin gerbes, tame Artin curves, and algebraic space surfaces, each of which we establish independently.

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