Related papers: Exotic t-structure for partial resolutions of the …
We prove a relative version of the fact that semiorthogonal decompositions of the bounded derived category of coherent sheaves are strongly constrained by the base locus of the canonical linear system. As an application we prove that the…
The author explains local and global model structures on higher orbifolds which are truncated \'{e}tale differentiable higher stacks, and discuss the application of the model structures to quantum cohomology of higher and derived orbifolds.
A sufficient condition of the convergence of an exotic formal series (a kind of power series with complex exponents) solution to an ODE of a general form is proposed.
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
In this paper, we study smooth complex projective varieties $X$ such that some exterior power $\bigwedge^r T_X$ of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two…
In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have…
We construct a mixed invariant of non-orientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including some exotic examples.
The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
We consider the exotic vortex equations on compact Riemann surfaces. These generalise the well-known Jackiw-Pi and Ambj{\o}rn-Olesen vortex equations and arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in…
To develop a constructive description of $\mathrm{Ext}$ in categories of coherent sheaves over certain schemes, we establish a binatural isomorphism between the $\mathrm{Ext}$-groups in Serre quotient categories $\mathcal{A}/\mathcal{C}$…
We propose a conjecture on the structure of the bounded derived category of coherent sheaves of the moduli space rank $2$ parabolic bundles on $\mathbb{P}^1$.
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a natural extriangulated structure.
This short note is a supplement to the previous article with the same title. Here we treat a conical symplectic variety obtained as a finite covering of a (not necessarily normal) nilpotent orbit closure of a complex semisimple Lie algebra.
We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…
We prove a formula for the intersection R-torsion of a finite cone and use it to introduce a family of spectral invariants which is closely related to Cheeger's half torsion.
We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and…
We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components…
This letter establishes a procedure which can determine an algebra of exotic particles obeying fractional statistics and living in two-dimensional space using a non-commuting coordinates.
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.