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  • [hal-01618799] Construction of Brauer-Severi Varieties

    18 octobre, par Elisa Lorenzo Garcia
    In this paper we give an algorithm for computing equations of Brauer-Severi varieties over perfect fields of characteristic 0. As an example we show the equations of all Brauer-Severi surfaces defined over $\mathbbQ$.
  • [hal-01618783] The Picard Group of Brauer-Severi Varieties

    18 octobre, par Eslam Badr, Francesc Bars, Elisa Lorenzo Garcia
    In this note we provide explicit generators of the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular, for all Brauer-Severi surfaces. To produce these generators we use the Twisting Theory for smooth plane (...)
  • [hal-01618759] On twists of smooth plane curves

    18 octobre, par Eslam Badr, Francesc Bars Cortina, Elisa Lorenzo Garcia
    Given a smooth curve defined over a field $k$ that admits a non-singular plane model over $\overlinek$, a fixed separable closure of $k$, it does not necessarily have a non-singular plane model defined over the field $k$. We determine under which conditions this happens and we show an example (...)
  • [hal-01618727] A note on the stratification by automorphisms of smooth plane curves of genus 6

    18 octobre, par Eslam Badr, Elisa Lorenzo García
    In this note, we give a so-called representative classification for the strata by automorphism group of smooth $\bark$-plane curves of genus $6$, where $\bark$ is a fixed separable closure of a field $k$ of characteristic $p = 0$ or $p > 13$. We start with a classification already obtained (...)
  • [hal-01618637] Computing twists of hyperelliptic curves

    18 octobre, par Davide Lombardo, Elisa Lorenzo García
    We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.

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