Related papers: Extremal contractions, stratified Mukai flops and …
We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other…
Negami's famous planar cover conjecture is equivalent to the statement that a connected graph can be embedded in the projective plane if and only if it has a projective planar cover. In 1999, Hlin\v{e}n\'y proposed extending this conjecture…
We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which…
For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations…
We describe the birational correspondences, induced by the Fourier-Mukai functor, between moduli spaces of semistable sheaves on elliptic surfaces with sections, using the notion of $P$-stability in the derived category. We give explicit…
In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the…
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is generally not preserved. For $A_{n, 2}$,…
We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane…
The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out…
Using pagoda flop transitions between smooth projective threefolds, a relation is derived between the Euler numbers of moduli spaces of stable pairs which are scheme-theoretically supported on a fixed singular space curve and Euler numbers…
Let $G$ be a connected algebraic group. We study $G$-equivariant extremal contractions whose centre is a codimension three $G$-simply connected orbit. In the spirit of an important result by Kawakita in 2001, we prove that those…
Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the…
We explain how to exploit systematically the structure of nilpotent orbits to obtain a solvable system of equations describing extremal solutions of (super-)gravity theories, i.e. systems that can be solved in a linear way. We present the…
In this paper we discuss some recent results about extremal contractions of complex algebraic varieties. These are proper surjective maps, $\phi: X\longrightarrow Z$, of normal varieties with connected fibers such that $X$ has mild…
An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…
The Coulomb branches of certain 3-dimensional N=4 quiver gauge theories are closures of nilpotent orbits of classical or exceptional algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been…
We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic…
We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra.
A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…