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

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

The transcendental lattice of the sextic Fermat surface

We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface is decomposable. This disproves a conjecture of Kulikov related to a Hodge theoretic approach to proving the irrationality of the very general cubic fourfold.Comment: 15 pages; v2: minor changes, streamlined the argument in Section

Abrasion Damage in Sediment Bypass Tunnels

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Recovery of Riverbed Features and Invertebrate Community in Degraded Channels by Sediment Supply through Bypass Tunnel

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Universal triviality of the Chow group of 0-cycles and the Brauer group

We prove that a smooth proper universally CH0-trivial variety X over a field k has universally trivial Brauer group. This fills a gap in the literature concerning the p-torsion of the Brauer group when k has characteristic p⁠

Conic bundle fourfolds with nontrivial unramified Brauer group

We derive a formula for the unramified Brauer group of a general class of rationally connected fourfolds birational to conic bundles over smooth threefolds. We produce new examples of conic bundles over P3 where this formula applies and which have nontrivial unramified Brauer group. The construction uses the theory of contact surfaces and, at least implicitly, matrix factorizations and symmetric arithmetic Cohen–Macaulay sheaves, as well as the geometry of special arrangements of rational curves in P2. We also prove the existence of universally CH0-trivial resolutions for the general class of conic bundle fourfolds we consider. Using the degeneration method, we thus produce new families of rationally connected fourfolds whose very general member is not stably rational

Sanierung des Gaulwerks – Variantenstudie unter Berücksichtigung von Umwelt, Sedimentmanagement und Hochwasserschutz

Aufsatz veröffentlicht in: "Wasserbau-Symposium 2021: Wasserbau in Zeiten von Energiewende, Gewässerschutz und Klimawandel, Zurich, Switzerland, September 15-17, 2021, Band 1" veröffentlicht unter: https://doi.org/10.3929/ethz-b-00049975