Related papers: A note on symplectic singularities

We further analyze the moduli space of stable curves with level structure provided by Chiodo and Farkas in \cite{AA}. Their result builds upon Harris and Mumford analysis of the locus of singularities of the moduli space of curves and shows…

Based on the Decay and Fission Conjecture, we provide a classification of unitary quivers whose 3d $\mathcal{N}=4$ Coulomb branches exhibit isolated singularities. This yields the complete list of isolated conical symplectic singularities…

We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…

We investigate the Hodge structure of the singular O'Grady's six and ten dimensional examples of irreducible symplectic varieties. In particular, we compute some of their Betti numbers and their Euler characteristic. As consequence, we…

For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities, and classify the…

We determine explicitly the irreducible components of the singular locus of any Schubert variety for GL_n(K), K being an algebraically closed field of arbitrary characteristic. We also describe the generic singularities along these…

We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with indefinite intersection forms which are not…

We describe the generic singularity of a Schubert variety of type A on each irreducible component of its singular locus. This singularity is given either by a cone of rank one matrices, or a quadratic cone.

The notion of strict singular characteristics is important in the wellposedness issue of singular dynamics on the cut locus of the viscosity solutions. We provide an intuitive and rigorous proof of the existence of the strict singular…

Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure…

Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up…

We review properties of affine special Kaehler structures focusing on singularities of such structures in the simplest case of real dimension two. We describe all possible isolated singularities and compute the monodromy of the flat…

We prove that the affine closure of the cotangent bundle of the basic affine space of a complex semisimple group has conical symplectic singularities, which confirms a conjecture of Ginzburg and Kazhdan. We also show that this variety is…

We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree $d = g - 1$, we characterize when the effective locus gives a Theta divisor. In case of degree $g - 2$…

Let $X\subset \mathbb{P}^4$ be a terminal factorial quartic $3$-fold. If $X$ is non-singular, $X$ is \emph{birationally rigid}, i.e. the classical MMP on any terminal $\mathbb{Q}$-factorial projective variety $Z$ birational to $X$ always…

In this article we consider integrable systems on manifolds endowed with singular symplectic structures of order one. These structures are symplectic away from an hypersurface where the symplectic volume goes either to infinity or to zero…

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of…

We study the GIT compactification $\mathbb{P}(\mathrm{Sym}^3\mathbb{C}^7)//\mathrm{SL}(7)$ of the moduli space of cubic fivefolds $X\subset\mathbb{P}^6$ and give an explicit description of its strictly semistable boundary. We construct…

A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$,…

We show that the natural symplectic structure on the Milnor fiber of an isolated singularity in complex three variables whose link fibers over the circle can be modified into one which is cylindrical at the end. As a consequence we see that…