Related papers: Deformations of Semi-Euler Characteristics

Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…

We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we study the geometry and Hodge theory of multivariable…

Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order…

We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

The aim of this note is to investigate characterizations and deformations of elliptic Calabi--Yau manifolds, building on earlier works of Wilson and Oguiso. Version 2: References updated and small changes. Version 3: Smoothness conditions…

Let $M$ be a complete Riemannian manifold possibly with a boundary $\partial M$. For any $C^1$-vector field $Z$, by using gradient/functional inequalities of the (reflecting) diffusion process generated by $L:=\Delta+Z$, pointwise…

We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.

In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for…

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

We introduce a notion of $Q$-algebra that can be considered as a generalization of the notion of $Q$-manifold (a supermanifold equipped with an odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on modules over…

Let $(M, \Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $\pi: M \to B$, and $\eta$ a closed $(1,1)$-form on $B$. Then $\Omega+ \pi^* \eta$ is a holomorphically symplectic form on a complex…

We construct deformation quantizations with separation of variables on a split super-K\"ahler manifold and describe their canonical supertrace densities.

In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated to simple Lie superalgebras and their universal…

Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions…

We shall develop a theory of multi-pointed non-commutative deformations of a simple collection in an abelian category, and construct relative exceptional objects and relative spherical objects in some cases. This is inspired by a work by…

We study deformation properties of balanced hyperbolicity, with a particular emphasis on degenerate balanced manifolds and their behavior under smooth modifications. From a different perspective, we introduce two new notions of…

We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just…

We construct two-parameter families of integrable $\lambda$-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric…