Results 21 to 30 of about 65 (58)
Anabelian aspects in the étale homotopy theory of Brauer-Severi varieties [PDF]
, 2013 We study the etale homotopy theory of Brauer-Severi varieties over fields of characteristic 0. We prove that the induced Galois representations on geometric homotopy invariants (e.g., l-adic cohomology or higher homotopy groups) are all isomorphic for Brauer-Severi varieties of the same dimension. If the base field has cohomological dimension smaller
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Morphisms to Brauer–Severi Varieties, with Applications to Del Pezzo Surfaces [PDF]
, 2017 We classify morphisms from proper varieties to Brauer–Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated invertible sheaves. As an application, we study del Pezzo surfaces of large degree with a view towards Brauer–Severi varieties, and recover classical results on rational ...
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First Steps towards Hyper-desingularization through Brauer-Severi Varieties
, 2005 Given a Cayley-Hamilton smooth order A in a central simple algebra $Σ$, we determine the flat locus of the Brauer-Severi fibration of the smooth order. Moreover, we give a classification of all (reduced) central singularities where the flat locus differs from the Azumaya locus and show that the fibers over the flat, non-Azumaya points near these ...
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Absolutely split locally free sheaves on Brauer–Severi varieties of index two
Bulletin des Sciences Mathématiques, 2012 The author classifies absolutely split locally free sheaves on Brauer-Severi varieties of index two. Recall that a scheme \(X\) over a field \(k\) is a Brauer-Severi variety if there is an isomorphism \(X\otimes_k \overline{k} \cong \mathbb{P}^n_{\overline{k}}\) for some integer \(n\).
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Morphisms to Brauer-Severi Varieties, with Applications to Del Pezzo Surfaces
, 2016 We classify morphisms from proper varieties to Brauer-Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated invertible sheaves. As an application, we study del Pezzo surfaces of large degree with a view towards Brauer-Severi varieties, and recover classical results on rational ...
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Non-split Brauer-Severi varieties do not admit full exceptional collections
, 2016 Recently, Novaković conjectured that non-split Brauer-Severi varieties do not admit full strong exceptional collections. In this short note, we explain how a stronger version of this conjecture follows easily from known results on noncommutative motives.
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Tilting Sheaves on Brauer-Severi Schemes and Arithmetic Toric Varieties [PDF]
, 2014 The derived category of coherent sheaves on a smooth projective variety is an important object of study in algebraic geometry. One important device relevant for this study is the notion of tilting sheaf. This thesis is concerned with the existence of tilting sheaves on some smooth projective varieties. The main technique we use in this thesis is Galois
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No full exceptional collections on non-split Brauer--Severi varieties of dimension $\leq 3$
, 2016 commetnts ...
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Brauer-Severi varieties associated to twists of the Burkhardt quartic
, 2020 The Burkhardt quartic is a projective threefold which, geometrically, is birational to the moduli space of abelian surfaces with full level-3 structure. We study this moduli interpretation of the Burkhardt quartic in an arithmetic setting, over a general field $k$.
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