Related papers: On the structure of instability in moduli theory

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…

We establish a Harder-Narasimhan formalism for modifications of $G$-bundles on the Fargues-Fontaine curve. The semi-stable stratum of the associated stratification of the $B_{dR}^+$-Grassmannian coincides with the variant of the weakly…

We study quadratic moduli schemes $X$ of algebra laws on a fixed vector space $W$ under the transport-of-structure action of $GL(W)$ on $Hom(W^{\otimes 2},W)$. We construct an intrinsic three-term deformation complex on $X$ whose fibers…

We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the…

For each $0<\alpha<\frac{1}{2}$, there exists a Bayer--Lahoz--Macr{\`{\i}}--Stellari inducing Bridgeland stability condition $\sigma(\alpha)$ on a Kuznetsov component $\mathrm{Ku}(Q)$ of the smooth quadric threefold $Q$. We obtain the…

We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived…

The Gaussian-filtered Navier-Stokes equations are examined theoretically and a generalized theory of their numerical stability is proposed. Using the exact expansion series of subfilter-scale stresses or integration by parts, the terms…

In [BM14b], the first author and Macr\`i constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated…

We construct, using geometric invariant theory, a quasi-projective Deligne-Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded A-infinity-algebras. The tangent…

We define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…

We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In…

We describe a new approach to the definition of the moduli functor of stable varieties. While there is wide agreement as to what classes of varieties should appear, the notion of a family of stable surfaces is quite subtle, as key numerical…

We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of…

We suggest to endow Mumford's GIT quotient scheme with a stack structure, by replacing Proj(-) of the invariant ring with its stack theoretic analogue. We analyse the stacks resulting in this way from classically studied invariant rings,…

We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry of supermanifolds to include a treatment of…

We give a generalisation of the theory of optimal destabilizing 1-parameter subgroups to non-algebraic complex geometry. Consider a holomorphic action $G\times F\to F$ of a complex reductive Lie group $G$ on a finite dimensional (possibly…