46 citations · 172 across the 25 of their papers we have counts for
27 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…
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…
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…
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 Jaco…
Derived categories of Fano threefolds and degenerations
Alexander Kuznetsov, Evgeny Shinder
Using the technique of categorical absorption of singularities we prove that the nontrivial components of the derived categories of del Pezzo threefolds of degree $d \in \{2,3,4,5\…
Derived equivalence of elliptic K3 surfaces and Jacobians
Reinder Meinsma, Evgeny Shinder
We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structure…
Homological Bondal-Orlov localization conjecture for rational singularities
Mirko Mauri, Evgeny Shinder
Given a resolution of rational singularities over a field of characteristic zero we use a Hodge-theoretic argument to prove that the image of the functor…
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,…
Motivic invariants of birational maps
Hsueh-Yung Lin, Evgeny Shinder
We construct invariants of birational maps with values in the Kontsevich--Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of g…
Categorical absorptions of singularities and degenerations
Alexander Kuznetsov, Evgeny Shinder
We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory respons…
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…
Factorization centers in dimension two and the Grothendieck ring of varieties
Hsueh-Yung Lin, Evgeny Shinder, Susanna Zimmermann
We initiate the study of factorization centers of birational maps, and complete it for surfaces over a perfect field in this article. We prove that for every birational automorphis…
Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory
Martin Kalck, Nebojsa Pavic, Evgeny Shinder
We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolate…
L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Evgeny Shinder, Ziyu Zhang
We construct nontrivial L-equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples o…
Variation of Stable Birational Types of Hypersurfaces
Evgeny Shinder, with an appendix by Claire Voisin
We introduce and study the question how can stable birational types vary in a smooth proper family. Our starting point is the specialization for stable birational types of Nicaise…
K-theory and the singularity category of quotient singularities
Nebojsa Pavic, Evgeny Shinder
In this paper we study Schlichting's K-theory groups of the Buchweitz-Orlov singularity category of a quasi-projective algebraic scheme with application…
Derived categories of singular surfaces
Joseph Karmazyn, Alexander Kuznetsov, Evgeny Shinder
We develop an approach that allows to construct semiorthogonal decompositions of derived categories of surfaces with cyclic quotient singularities whose components are equivalent t…
The motivic nearby fiber and degeneration of stable rationality
Johannes Nicaise, Evgeny Shinder
We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic s…
Group actions on categories and Elagin's Theorem Revisited
Evgeny Shinder
After recalling basic definitions and constructions for a finite group action on a -linear category we give a concise proof of the following theorem of Elagin: if $\mathcal{…
Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics
Alexander Kuznetsov, Evgeny Shinder
We discuss a conjecture saying that derived equivalence of simply connected smooth projective varieties implies that the difference of their classes in the Grothendieck ring of var…
The Bogomolov-Prokhorov invariant of surfaces as equivariant cohomology
Evgeny Shinder
For a complex smooth projective surface with an action of a finite cyclic group we give a uniform proof of the isomorphism between the invariant $H^1(G, H^2(M, {\mathbb Z})…
On automorphic forms of small weight for fake projective planes
Sergey Galkin, Ilya Karzhemanov, Evgeny Shinder
On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-to…
On the geometry of the LLSvS eightfold
Evgeny Shinder, Andrey Soldatenkov
In this note we make a few remarks about the geometry of the holomorphic symplectic manifold Z constructed by C.Lehn, M.Lehn, C.Sorger and D. van Straten as a two-step contraction…
On a zeta-function of a dg-category
Sergey Galkin, Evgeny Shinder
We define a zeta-function of a pre-triangulated dg-category and investigate its relationship with the motivic zeta-function in the geometric case.