Related papers: Note on double reflection and algebraicity of holo…
Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking…
We show the following algebraicity result for a complex projective variety $X$ with big representation of $\pi_1$ into a semi-simple algebraic group: There exists a proper subvariety $Z \subset X$ such that for any algebraic curve $C$, any…
We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations…
We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…
A number of issues in heterotic double field theory are studied. This includes the analysis of the T-dual configurations of a flat constant gauge flux background, which turn out to be non-geometric. Performing a field redefinition to a…
The supercoonformal index on $\mathbb{RP}^{2} \times \mathbb{S}^{1}$ can be derived exactly by the localization technique and applied to the direct proof of Abelian mirror symmetry. We find two sets of parity conditions compatible with the…
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We…
We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.
Algebraic hyperbolicity serves as a bridge between differential geometry and algebraic geometry. Generally, it is difficult to show that a given projective variety is algebraically hyperbolic. However, it was established recently that a…
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as…
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…
We give a combinatorial characterization of generic minimally rigid reflection frameworks. The main new idea is to study a pair of direction networks on the same graph such that one admits faithful realizations and the other has only…
We show that for any smooth Hausdorff manifolds M and N, which are not necessarily second countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on…