1,405 research outputs found
Stable rationality of quadric and cubic surface bundle fourfolds
We study the stable rationality problem for quadric and cubic surface bundles
over surfaces from the point of view of the degeneration method for the Chow
group of 0-cycles. Our main result is that a very general hypersurface X of
bidegree (2,3) in P^2 x P^3 is not stably rational. Via projections onto the
two factors, X is a cubic surface bundle over P^2 and a conic bundle over P^3,
and we analyze the stable rationality problem from both these points of view.
This provides another example of a smooth family of rationally connected
fourfolds with rational and nonrational fibers. Finally, we introduce new
quadric surface bundle fourfolds over P^2 with discriminant curve of any even
degree at least 8, having nontrivial unramified Brauer group and admitting a
universally CH_0-trivial resolution.Comment: 27 pages, comments welcome
Gaps in Basic Workers’ Rights: Measuring International Adherence to and Implementation of the Organization’s Values With Public ILO Data
Conceptualizes and measures numerically the gap between the real and the ideal world of basic workers’ rights with the help of the ratification, reporting, supervisory and complaints data at the disposal of the ILO
Stable rationality of quadric and cubic surface bundle fourfolds
We study the stable rationality problem for quadric and cubic surface bundles
over surfaces from the point of view of the degeneration method for the Chow
group of 0-cycles. Our main result is that a very general hypersurface X of
bidegree (2,3) in P^2 x P^3 is not stably rational. Via projections onto the
two factors, X is a cubic surface bundle over P^2 and a conic bundle over P^3,
and we analyze the stable rationality problem from both these points of view.
This provides another example of a smooth family of rationally connected
fourfolds with rational and nonrational fibers. Finally, we introduce new
quadric surface bundle fourfolds over P^2 with discriminant curve of any even
degree at least 8, having nontrivial unramified Brauer group and admitting a
universally CH_0-trivial resolution.Comment: 27 pages, comments welcome
On stable rationality of some conic bundles and moduli spaces of Prym curves
We prove that a very general hypersurface of bidegree (2, n) in P^2 x P^2 for
n bigger than or equal to 2 is not stably rational, using Voisin's method of
integral Chow-theoretic decompositions of the diagonal and their preservation
under mild degenerations. At the same time, we also analyse possible ways to
degenerate Prym curves, and the way how various loci inside the moduli space of
stable Prym curves are nested. No deformation theory of stacks or sheaves of
Azumaya algebras like in recent work of Hasset-Kresch-Tschinkel is used, rather
we employ a more elementary and explicit approach via Koszul complexes, which
is enough to treat this special case.Comment: 23 pages; Macaulay 2 code used for verification of parts of the paper
available at http://www.math.uni-hamburg.de/home/bothmer/m2.html and at the
end of the TeX file; v2: in section 4, we now included a proof of the main
theorem that works for all n (unconditional on the parity) that was
communicated to us by Zhi Jiang, Zhiyu Tian, and Letao Zhang. Several other
minor expository improvement
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