Strong approximation for a toric variety

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August undefined, 2024

WebWe prove that X\setminus W satisfies strong approximation with algebraic Brauer--Manin obstruction. Let X be a toric variety over a number field k with … Webproved any toric variety X satisﬁes strong approximation with Brauer–Manin obstruction oﬀ all inﬁnite places (without k[X]× = k×). However, if k[X]× = k×, generally X \ W does not …

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WebLet X be a smooth and geometrically integral variety over a number field k. Suppose X contains a torus and ¯¯¯k[X]×=¯¯¯k×, let W⊂X be a closed subset of codimension at least … Webplay in putting sufﬁciently strong conditions on our moduli spaces. 1.2 Outline Generally, log structures are useful for remembering information about a scheme which is not ... Abstractly, a projective toric variety is a projective variety together with the action of a torus. The torus Tnis deﬁned to be the product of ncopies of the ... mark layton scrum

Strong approximation with Brauer-Manin obstruction for toric …

WebSTRONG APPROXIMATION FOR A TORIC VARIETY DASHENG WEI ABSTRACT. Let X be a toric variety over a number ﬁeld k with k[X]× =k ×. Let W ⊂ X be a closed subset of … WebMar 5, 2014 · Strong approximation for the variety containing a torus March 2014 Source arXiv Authors: Dasheng Wei Chinese Academy of Sciences Request full-text Abstract Let X be a smooth and geometrically... WebMar 5, 2014 · Suppose X contains a torus and \kbar[X]^\times=\kbar^\times. In this note, we proved that X satisfies strong approximation with etale Brauer--Manin obstruction off one … navy credit federal union branch location s

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W H A T I S . . . a Toric Variety?

WebEvery toric variety has a ﬁnite open cover by aﬃne toric varieties; hence torus orbit closures in Cn are, in a toric sense, locally universal. The parametrized view of (not necessarily aﬃne) toric varieties is key in applications to geometric modeling, because every polynomial parametrization of a space is the projection of a monomial one. Webdermild hypotheses, every point on asmooth variety is conjecturally canonically bounded: Proposition 1.3. Let X be a smooth projective variety over a number ﬁeld k, and let P ∈X(k) be a k-rational point. Assume that there is an ample divisor A on X for which α P(A) is ﬁnite. Then Vojta’s Main Conjecture implies that X is ... mark layton mammoth energyWebDec 1, 2024 · In particular, we give a new proof of strong approximation for quasi-split semi-simple simply connected groups by establishing fibrations over toric varieties. Theorem 1.1 Theorem 3.6 Let G be a semi-simple simply connected and quasi-split group over a number field k and S ≠ ∅ be a finite set of places of k. mark lazarus horry county

"WebJan 15, 2024 · Strong Approximation for a Toric Variety January 2024 Authors: Da Sheng Wei Abstract Let X be a toric variety over a number field k with k̅ [X]× = k̅×. Let W ⊂ X be a … " - Strong approximation for a toric variety

Strong approximation for a toric variety

WebThe answer is ‘yes’ whenXis a projective toric variety over C. As a corollary, we shall prove that the smooth loci of projective toric varieties over Cis strongly rationally connected. Advisor : Professor Vyacheslav Shokurov Readers: Professor Vyacheslav Shokurov, Professor Steven Zucker ii ACKNOWLEDGEMENTS WebJul 19, 2024 · We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of...

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Webprojective Q-factorial variety X, that satis es Pic(X)Q = N1(X)Q and has a nitely generated Cox ring (see De nition II.13). One basic example is that of toric varieties, in which the Cox ring is a polynomial ring in nitely many variables (see [Cox95]). Thus, a projective simplicial toric variety is a Mori dream space. Another example is Webvariety X= X(F). It is not hard to see that the natural action of the torus corresponding to the zero cone extends to an action on the whole of X. Therefore X(F) is indeed a toric variety. Let us look at some examples. Example 11.3. Suppose that we start with M= Z and we let Fbe the fan given by the three cones f0g, the cone spanned by e 1 and ...

WebLet X be a toric variety over a number field k with \kbar[X]^\times=\kbar^\times. Let W\subset X be a closed subset of codimension at least 2. We prove that X\setminus W … WebLet X be a smooth and geometrically integral variety over a number field k. Suppose X contains a torus and ¯¯¯k[X]×=¯¯¯k×, let W⊂X be a closed subset of codimension at least 2. In this note, we proved that X∖W satisfies strong approximation with étale algebraic Brauer–Manin obstruction off one place. Furthermore, if Pic(¯¯¯¯¯X) is torsion free, then …

WebFor example, any torus is a toric variety. An k is a toric variety. The natural torus is the complement of the coordinate hyperplanes and the natural action is as follows ((t 1;t 2;:::;t n);(a 1;a 2;:::;a n)) ! (t 1a 1;t 2a 2;:::;t na n): More generally, Pn is a toric variety. The action is just the natural action induced from the action above ... Webhigher dimensional split toric varieties. Given a split toric variety Xover a number eld k, we say f: Xe!Xis a terminal resolution if it is a proper birational toric morphism de ned over kand Xeis Q-factorial, projective, and has at worst terminal singularities. Theorem 1.5. Let X be a split toric variety over a number eld k and let P 2X(k).

Web1 From combinatorial geometry to toric varieties The procedure of the construction of (aﬃne) toric varieties associates to a cone σ in the Euclidean space Rn successively: the dual cone ˇσ, a monoid S σ, a ﬁnitely generated C-algebra R σ and ﬁnally an algebraic variety X σ. In the following, we describe the steps of this procedure ...

WebLempert theory. We show that an aﬃne toric variety X satisﬁes this algebraic density property relative to a closed T-invariant subvariety Y if and only if X\Y 6= T. For toric surfaces we are able to classify those which posses a strong version of the algebraic density property (relative to the singular locus). mark layton raytheonWeb— For smooth open toric varieties, we establish strong approximation off infinity with Brauer–Manin obstruction. Résumé. — Pour les variétés toriques lisses ouvertes, on … mark layton brown farrah forkeWebMay 22, 2024 · Parameterized toric codes includes toric codes, constructed by Hansen in [ 9 ], as a special case where Q is the identity matrix I_r and Y_Q is the full torus T_X. Toric codes are among evaluation codes on a toric variety showcasing champion examples, see [ 1, 2, 12 ]. The length in this special case is T_X = (q-1)^n. mark lazarus cape townWebToric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. mark lazarus horry county councilWebMar 5, 2014 · Abstract: Let X be a toric variety over a number field k with \kbar[X]^\times=\kbar^\times. Let W\subset X be a closed subset of codimension at least … mark lazarus the athleticWebJul 16, 2024 · We prove that X \ W satisfies strong approximation with algebraic Brauer-Manin obstruction. Let X be a toric variety over a number field k with k̅ [ X ] × = k̅ × . Let W … navy credit federal union locationsWebJun 27, 2012 · We say that an affine variety X ⊆ℂ r is toric if it allows an (algebraic) action of a torus \mathbb {T}^ {n} such that we can identify \mathbb {T}^ {n} via the orbit map with some open dense orbit \mathbb {T}^ {n} \cdot x_ {0} \subseteq X. For example, the two Veronese/Segre quadrics just mentioned are toric: navy credit federal union login