On the classification of singularities that are equivariant simple with respect to representations of cyclic groups

E.A. Astashov;

doi:10.20537/vm160201

On the classification of singularities that are equivariant simple with respect to representations of cyclic groups

Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki ◽

10.20537/vm160201 ◽

2016 ◽

Vol 26 (2) ◽

pp. 155-159 ◽

Cited By ~ 2

Author(s):

E.A. Astashov ◽

Keyword(s):

Cyclic Groups ◽

Classification Of Singularities

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Construction and classification of holomorphic vertex operator algebras

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2017-0046 ◽

2020 ◽

Vol 2020 (759) ◽

pp. 61-99 ◽

Cited By ~ 8

Author(s):

Jethro van Ekeren ◽

Sven Möller ◽

Nils R. Scheithauer

Keyword(s):

Vertex Operator ◽

Operator Algebras ◽

Central Charge ◽

Field Theories ◽

Vertex Operator Algebras ◽

Conformal Field Theories ◽

Cyclic Groups ◽

Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

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Quotients of del Pezzo surfaces

International Journal of Mathematics ◽

10.1142/s0129167x1950068x ◽

2019 ◽

Vol 30 (12) ◽

pp. 1950068

Author(s):

Andrey Trepalin

Keyword(s):

Complete Classification ◽

Finite Subgroup ◽

Del Pezzo Surfaces ◽

Picard Number ◽

Del Pezzo Surface ◽

Cyclic Groups ◽

Trivial Group ◽

Quotient Surface ◽

Del Pezzo

Let [Formula: see text] be any field of characteristic zero, [Formula: see text] be a del Pezzo surface and [Formula: see text] be a finite subgroup in [Formula: see text]. In this paper, we study when the quotient surface [Formula: see text] can be non-rational over [Formula: see text]. Obviously, if there are no smooth [Formula: see text]-points on [Formula: see text] then it is not [Formula: see text]-rational. Therefore, under assumption that the set of smooth [Formula: see text]-points on [Formula: see text] is not empty we show that there are few possibilities for non-[Formula: see text]-rational quotients. The quotients of del Pezzo surfaces of degree [Formula: see text] and greater are considered in the author’s previous papers. In this paper, we study the quotients of del Pezzo surfaces of degree [Formula: see text]. We show that they can be non-[Formula: see text]-rational only for the trivial group or cyclic groups of order [Formula: see text], [Formula: see text] and [Formula: see text]. For the trivial group and the group of order [Formula: see text], we show that both [Formula: see text] and [Formula: see text] are not [Formula: see text]-rational if the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. For the groups of order [Formula: see text] and [Formula: see text], we construct examples of both [Formula: see text]-rational and non-[Formula: see text]-rational quotients of both [Formula: see text]-rational and non-[Formula: see text]-rational del Pezzo surfaces of degree [Formula: see text] such that the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. As a result of complete classification of non-[Formula: see text]-rational quotients of del Pezzo surfaces we classify surfaces that are birationally equivalent to quotients of [Formula: see text]-rational surfaces, and obtain some corollaries concerning fields of invariants of [Formula: see text].

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