Related papers: On braid monodromy factorizations
Given a smooth, projective curve $Y$, a point $y_0 \in Y$, a positive integer $n$, and a transitive subgroup $G$ of the symmetric group $S_{d}$ we study smooth, proper families, parameterized by algebraic varieties, of pointed degree $d$…
Every smooth minimal complex algebraic surface of general type, $X$, may be mapped into a moduli space, $\MM_{c_1^2(X), c_2(X)}$, of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful…
We classify semisimple rigid monoidal categories with two isomorphism classes of simple objects over the field of complex numbers. In the appendix written by P.Etingof it is proved that the number of semisimple Hopf algebras with a given…
We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides…
The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface. Calculating this factorization is of high technical…
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…
In this paper we give an algorithm for solving a main case of the conjugacy problem in the braid groups. We also prove that half-twists satisfy a special root property which allows us to reduce the solution for the conjugacy problem in…
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…
For each nonnegative integer $g$, we classify the ramification types and monodromy groups of indecomposable coverings of complex curves $f: X\to Y$ where $X$ has genus $g$, under the hypothesis that $n:=\deg(f)$ is sufficiently large and…
A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All…
We consider two families of categories. The first is the family of semisimple quotients of H. Andersen's tilting module categories for quantum groups of Lie type $B$ specialized at odd roots of unity. The second consists of categories…
On \'etudie la possibilit\'e de construire des solutions alg\'ebriques partielles des \'equations d'isomonodromie pour les connections holomorphes de rang $2$ sur les courbes de genre $2$ en adaptant la m\'ethode d'Andreev et Kitaev par les…
We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic polynomial over a field of characteristic different from two. This is a self-similar closed subgroup of the group of…
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if…
We show that if we are given a smooth non-isotrivial family of elliptic curves over~$\mathbb C$ with a smooth base~$B$ for which the general fiber of the mapping $J\colon B\to\mathbb A^1$ (assigning $j$-invariant of the fiber to a point) is…
We construct braided versions $sV_{br}$ of the Brin-Thompson groups $sV$ and prove that they are of type $F_\infty$. The proof involves showing that the matching complexes of colored arcs on surfaces are highly connected.
Let (S, B) be the log pair associated with a projective completion of a smooth quasi-projective surface V . Under the assumption that the boundary B is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…