Real rational surfaces

Mangolte, Frederic

doi:10.48550/arxiv.1503.01248

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…Roughly speaking, disentangling the degrees of freedom between two copies of field theory implies, on the geometry side, a transition from a nonorientable spacetime to a spacetime having a definite ori-entation of space and time, thus an orientable spacetime. Therefore, starting with initial high-correlation and disentangling the degrees of freedom is consistent, in the geometrical dual, to a topological blow down operation [23], [24], [25], [26]. Since disentangling the degrees of freedom between regions is equivalent to a topological blow down, we conclude that the change in topology is an abrupt transition from a non-orientable spacetime to an orientable spacetime.…”

Section: Introductionmentioning

confidence: 69%

Quantum entanglement and the non-orientability of spacetime

Racorean¹

2020

Preprint

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We argue, in the context of Ads/CFT correspondence, that the degree of entanglement on the CFTs side determines the orientation of space and time on the dual global spacetime. That is, the global spacetime dual to entangled copies of field theory is non-orientable, while the product state of the CFTs results in an orientable spacetime. As a result, disentangling the degrees of freedom between two copies of CFT implies, on the gravity side, the transition from a non-orientable spacetime to a spacetime having a definite orientation of space and time, thus an orientable spacetime. We conclude showing that topology change induced by decreasing the entanglement between two sets of degrees of freedom corresponds to a topological blow down operation.

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Section: Introductionmentioning

confidence: 69%

Quantum entanglement and the non-orientability of spacetime

Racorean¹

2020

Preprint

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“…More generally, it is a striking result of Biswas and Huisman [3](see also [17]) that all rational algebraic complexifications of a given smooth compact surface M are all R-biregularly birationally equivalent: this means that for every pair V and V of such complexifications, there exists birational maps ϕ : V V and ϕ : V V inverse to each other and whose restrictions to the real loci of V and V are diffeomorphisms inverse to each other. This classification result gave rise to many further discoveries, see the survey article [23] and the bibliography given there. In addition to RP 2 , the compact surfaces M diffeomorphic to the real locus of smooth rational projective surface minimal over R are the sphere S 2 , the torus S 1 × S 1 and the Klein bottle K = RP 2 #RP 2 .…”

Section: Introductionmentioning

confidence: 79%

Fake Real Planes: exotic affine algebraic models of $\mathbb{R}^{2}$

Dubouloz,

Mangolte

2015

Preprint

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We study real rational models of the euclidean affine plane R 2 up to isomorphisms and up to birational diffeomorphisms. The analogous study in the compact case, that is the classification of real rational models of the real projective plane RP 2 is well known: up to birational diffeomorphisms, P 2 (R) is the only model. A fake real plane is a smooth geometrically integral surface S defined over R not isomorphic to A 2 R , whose real locus S(R) is diffeomorphic to R 2 and such that the complex surface S C (C) has the rational homology type of A 2 C . We prove that fake planes exist by giving many examples and we tackle the question: does there exist fake planes S such that S(R) is not birationally diffeomorphic to A 2 R (R)?

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“…It is well-known that every rational projective complexification of RP 2 is R-biregularly birationally equivalent to RP 2 , even dropping the topological minimality condition, see [17]. Thus next natural questions are: Question 4.…”

Section: Introductionmentioning

confidence: 99%

Real frontiers of fake planes

Dubouloz

Mangolte

2015

European Journal of Mathematics

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Abstract. In [8], we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane R 2 . Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this note, we describe in an elementary way numerous examples of fake real planes and we exhibit examples of such planes of every Kodaira dimension κ ∈ {−∞, 0, 1, 2} which are birationally diffeomorphic to R 2 .

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Real rational surfaces

Abstract: With the exception of some classical references, only references over the past years from the preceding "RAAG conference in Rennes", which took place in 2001, are included.

Cited by 3 publications

References 21 publications

Quantum entanglement and the non-orientability of spacetime

Quantum entanglement and the non-orientability of spacetime

Fake Real Planes: exotic affine algebraic models of $\mathbb{R}^{2}$

Real frontiers of fake planes

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