Related papers: Deforming Stanley-Reisner schemes
The versal deformation of Stanley-Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
We give a geometric interpretation of the Stanley--Reisner correspondence, extend it to schemes, and interpret it in terms of the field of one element.
In this paper we give a description of the first order deformation space of a regular embedding of reduced algebraic schemes. We compare our result with results of Ran (in particular [Ran, Prop. 1.3]).
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.
A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…
We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.
A representation of generalized Weierstrass formulae for an immersion of generic surfaces into a 4-dimensional complex space in terms of spinors treated as minimal left ideals of Clifford algebras is proposed. The relation between…
In this paper, we study obstructed and unobstructed (holomorphic) Poisson deformations with classical examples in deformation theory.
We give an exposition of the formal aspects of deformation theory in the language of fibered categories, instead of the more traditional one of functors. The main concepts are that of tangent space to a deformation problem, obstruction…
An odd deformation of a super Riemann surface $\mathcal S$ is a deformation of $\mathcal S$ by variables of odd parity. In this article we study the obstruction theory of these odd deformations $\mathcal X$ of $\mathcal S$. We view…
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of Delaunay tessellation. We use some of the ideas to study…
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded…
This paper proves a deformation circle pattern theorem, which gives a complete description of those circle patterns with interstices in terms of the combinatorial type, the exterior intersections angles and the conformal structures of…
In this paper we study the deformation theory of submanifolds characterized by a system of differential forms and provide a criterion for deformations of such submanifolds to be unobstructed. We apply this deformation theory to special…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
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…
This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…