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# Search by event  2101 | enregistrements trouvés : 5

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## Post-edited  ​On the Lüroth problem for real varieties Benoist, Olivier (Auteur de la Conférence) | CIRM (Editeur )

The Lüroth problem asks whether every unirational variety is rational. Over the complex numbers, it has a positive answer for curves and surfaces, but fails in higher dimensions. In this talk, I will consider the Lüroth problem for real algebraic varieties that are geometrically rational, and explain a counterexample not accounted for by the topology of the real locus or by unramified cohomology. This is joint work with Olivier Wittenberg.

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## Multi angle  Stably irrational hypersurfaces of small slopes Schreieder, Stefan (Auteur de la Conférence) | CIRM (Editeur )

We show that over any uncountable field of characteristic different from two, a very general hypersurface of dimension $n > 2$ and degree at least $log_2 (n) + 2$ is not stably rational. This significantly improves earlier results of Kollár and Totaro. As a byproduct of our proof, we obtain new counterexamples to the integral Hodge conjecture, answering a question of Voisin and Colliot-Thélène - Voisin.

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## Multi angle  On the B-Semiampleness Conjecture Floris, Enrica (Auteur de la Conférence) | CIRM (Editeur )

An lc-trivial fibration $f : (X, B) \to Y$ is a fibration such that the log-canonical divisor of the pair $(X, B)$ is trivial along the fibres of $f$. As in the case of the canonical bundle formula for elliptic fibrations, the log-canonical divisor can be written as the sum of the pullback of three divisors: the canonical divisor of $Y$; a divisor, called discriminant, which contains informations on the singular fibres; a divisor, called moduli part, that contains informations on the variation in moduli of the fibres. The moduli part is conjectured to be semiample. Ambro proved the conjecture when the base $Y$ is a curve. In this talk we will explain how to prove that the restriction of the moduli part to a hypersurface is semiample assuming the conjecture in lower dimension. This is a joint work with Vladimir Lazić.
An lc-trivial fibration $f : (X, B) \to Y$ is a fibration such that the log-canonical divisor of the pair $(X, B)$ is trivial along the fibres of $f$. As in the case of the canonical bundle formula for elliptic fibrations, the log-canonical divisor can be written as the sum of the pullback of three divisors: the canonical divisor of $Y$; a divisor, called discriminant, which contains informations on the singular fibres; a divisor, called moduli ...

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## Multi angle  Arithmetic of rank one local systems Esnault, Hélène (Auteur de la Conférence) | CIRM (Editeur )

Joint with Moritz Kerz. We study arithmetic subvarieties of the character variety of normal complex varieties defined over a field of finite type.

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## Multi angle  ​Absolute sets and the Decomposition Theorem Budur, Nero (Auteur de la Conférence) | CIRM (Editeur )

We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang.

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