Related papers: On the deformation chirality of real cubic fourfol…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, \ie, the polarization, exceptional divisors, and real structure recorded in the homology…
Given a family of stable curves, we define a sheaf of factorization algebras associated to any universal factorization algebra, and prove a gluing formula for the corresponding sheaf of chiral homology, generalizing the sheaves of vertex…
We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real Tate-Shafarevich group and reduce the deformation classification to the combinatorics of a…
This is the second in a series of papers on a new equivariant cohomology that takes values in a vertex algebra. In an earlier paper, the first two authors gave a construction of the cohomology functor on the category of O(sg) algebras. The…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…
We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…
In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$…
Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and…
Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} = *C $ independent of $B$ via the Hodge duality $*$. We show that the doubling of…
We compactify the spaces $K(m,n)$ introduced by Maxim Kontsevich. The initial idea was to construct an $L_\infty$ algebra governing the deformations of a (co)associative bialgebra. However, this compactification leads not to a resolution of…
We construct an invariant of closed ${\rm spin}^c$ 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a…
A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic $\sigma$-model, by a particular heterotic gauge field. This is inspired by the bosonic part of…
We introduce a four-term long exact sequence that relates the cohomology of a smooth variety admitting a projective morphism onto a projective base to the cohomology of the open set obtained by removing the preimage of a general linear…
Concerning the problem of classifying complete submanifolds of Euclidean space with codimension two admitting genuine isometric deformations, until now the only known examples with the maximal possible rank four are the real Kaehler minimal…
We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over a field of characteristic 0 and $\sigma\in…
The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra which depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty$ algebra…
We consider unitary cocycle deformations of covariant $\ast$-differential calculi. We prove that complex structures, holomorphic bimodules and Chern connections on the deformed calculus are twists of their untwisted counterparts. Moreover,…
We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in $\mathbb{C}^3$ of 2-dimensional general quadrics with…