Related papers: Factorization of point configurations, cyclic cove…

We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves…

We consider the following question: for which invariants $g$ and $e$ is there a geometrically ruled surface $S \rightarrow C$ over a curve $C$ of genus $g$ with invariant $e$ such that $S$ is the support of an Ulrich line bundle with…

We define a normed matrix factorization category and a notion of bounding cochains for objects of this category. We classify bounding cochains up to gauge equivalence for spherical objects and use this classification to define numerical…

We apply the theory of $\alpha$-induction of sectors which we elaborated in our previous paper to several nets of subfactors arising from conformal field theory. The main application are conformal embeddings and orbifold inclusions of SU(n)…

We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem…

Let $X$ be a smooth irreducible projective curve of genus $g \geq 2$ over a finite field $\F_{q}$ of characteristic $p$ with $q$ elements such that the function field $\F_{q}(X)$ is a geometric Galois extension of the rational function…

Given a projective family of semi-stable curves over a complete discrete valuation ring of characteristic p with algebraically closed residue field, we construct a specialization functor between the category of continuous representations of…

The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal…

We define and study a certain category of vector bundles on a p-adic curve to which we can associate in a functorial way finite dimensional p-adic representations of the geometric fundamental group. Among other things we investigate two…

Painlev\`e equation for conformal blocks is a combined corollary of integrability and Ward identities, which can be explicitly revealed in the matrix model realization of AGT relations. We demonstrate this in some detail, both for…

We study the Severi variety $V_{d,g}$ of plane curves of degree $d$ and geometric genus $g$. Corresponding to every such variety, there is a one-parameter family of genus $g$ stable curves whose numerical invariants we compute. Building on…

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…

For a manifold $W$ and an $E_d$-algebra $A$, the factorisation homology $\int_W A$ can be seen as a generalisation of the classical configuration space of labelled particles in $W$. It carries an action by the diffeomorphism group…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

Consider genus $g$ curves that admit degree $d$ covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family $Y$ that naturally maps into the moduli space of…

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…

We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to…

We give complete geometric invariants of cobordisms of framed fold maps. These invariants consist of two types. We take the immersion of the fold singular set into the target manifold together with information about non-triviality of the…

We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space of marked degree $d$ coverings of $\mathbb P^1$ of fixed…

An explicit invariant-theoretic description of the moduli space $\mathcal{M}_3^1$ of degree-three rational maps on $\mathbb{P}^1$ is developed. A cubic map $\phi$ is represented, up to conjugation, by the pair of binary forms $(f, g) \in…