Related papers: Examples of limits of Frobenius (type) structures:…

We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3-fold that is not a homogeneous space of an algebraic…

The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even…

We show that the equivalence between several possible characterizations of Frobenius algebras, and of symmetric Frobenius algebras, carries over from the category of vector spaces to more general monoidal categories. For Frobenius algebras,…

For every finite collection C of abelian varieties over F_q, we produce an explicit upper bound on the genus of curves over F_q whose Jacobians are isogenous to a product of powers of elements of C.

In this article we describe three constructions of complex variations of Hodge structure, proving the existence of interesting opposite filtrations that generalize a construction of Deligne. We also analyze the relation between deformations…

We study the problem of variation of Frobenius eigenvalues on the cohomology of families of local systems of algebraic curves over finite fields.

We show boundedness of $3$-folds of $\epsilon$-Fano type with Mori fibration structures. The proof is based on the birational boundedness result in our previous work arXiv:1509.08722 combining with arguments in Kawamata \cite{K} and…

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…

Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.

Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…

The theory of Frobenius groups with Frobenius complements of even order largely reduces to tractable algebraic number theory. If we consider only Frobenius complements with an upper bound $s$ on the number of distinct primes dividing the…

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual…

Given a singular foliation satisfying locally everywhere the Frobenius condition, even at the singularities, we show how to construct its global sheaves of jets. Our construction is purely formal, and thus applicable in a variety of…

We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

We describe a new infinite family of line arrangements in the projective plane with only triple points singularities and recover previously known examples.

We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.

We show that it makes sense to speak of THE Frobenius manifold attached to a convenient and nondegenerate Laurent polynomial

We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical…