Related papers: On equivariant formal deformation theory

In the first part of the paper we survey several results from Popa's deformation/rigidity theory on the classification of tensor product decompositions of large natural classes of II$_1$ factors. Using a m\'elange of techniques from…

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T^1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y…

Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation \beta, and a quaternary equidistance relation \equiv. Tarski established, inter alia, that the first-order…

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

In this article we present a unified way to smooth certain multiple structures called ropes on smooth varieties. We prove that most ropes of arbitrary multiplicity, supported on smooth curves can be smoothed. By a rope being smoothable we…

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…

A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its \'etale endomorphisms are proper. We study the conjecture for $\mathbb{Q}$-acyclic surfaces of negative Kodaira dimension. We show that $G$-equivariant…

Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number…

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…

We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…

We show that deformations of a surjective morphism onto a Fano manifold of Picard number 1 are unobstructed and rigid modulo the automorphisms of the target, if the variety of minimal rational tangents of the Fano manifold is non-linear or…

Let $X$ be a smooth algebraic variety endowed with an action of a finite group $G$ such that there exists the geometric quotient $\pi_X:X\to X/G$. We characterize rational tensor fields $\tau$ on $X/G$ such that the {\it pull back} of $\tau…

We prove several vanishing theorems for a class of generalized elliptic genera on foliated manifolds, by using classical equivariant index theory. The main techniques are the use of the Jacobi theta-functions and the construction of a new…

We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised tori, such as $L$-groups of (possibly non-split) tori. We show that the corresponding deformation rings are formally smooth over a…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

In this paper we investigate the Kodaira dimension of almost complex $4$-manifolds with torsion first Chern class. First, we prove that, if the almost complex structure is also tamed, the only possible values for the Kodaira dimension are…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We…

We show that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge D-modules on abelian varieties.