7 papers
Obstructions for codimension one multiple fibers of Lagrangian and Calabi--Yau fibrations
Yoon-Joo Kim, Keiji Oguiso, Evgeny Shinder
We prove that compact hyper-Kähler manifolds with a Lagrangian fibration over a projective space have no multiple fibers in codimension one. This has several consequences for the s…
Unboundedness for motivic invariants of birational automorphisms
Hsueh-Yung Lin, Evgeny Shinder
We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the…
Atomic decompositions for derived categories of G-surfaces
Alexey Elagin, Julia Schneider, Evgeny Shinder
We construct canonical semi-orthogonal decompositions for derived categories of smooth projective surfaces. These decompositions are compatible with the operations in the minimal m…
Twists of intermediate Jacobian fibrations
Yajnaseni Dutta, Dominique Mattei, Evgeny Shinder
We study the sections, Tate--Shafarevich twists, and the period for an OG10 hyperkähler Lagrangian associated to a cubic fourfold. To do so, we introduce the analytic relative Jac…
Derived categories of nodal del Pezzo threefolds
Nebojsa Pavic, Evgeny Shinder
We give a complete answer for the existence of Kawamata type semiorthogonal decompositions of derived categories of nodal del Pezzo threefolds. More precisely, we show that nodal d…
Homologically finite-dimensional objects in triangulated categories
Alexander Kuznetsov, Evgeny Shinder
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity,…