Related papers: The canonical pencils on Horikawa surfaces
We give a list of monodromy factorizations in the pure mapping class group $Mod(T_{d+1})$ of a torus with d+1 marked points that represent lines on a del Pezzo surface Y of degree $d\le4$. These factorizations are lifts of a certain fixed…
This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid…
This set of lectures aims to give an overview of Donaldson's theory of linear systems on symplectic manifolds and the algebraic and geometric invariants to which they give rise. After collecting some of the relevant background, we discuss…
We give a new proof - not using resolution of singularities - of a formula of Denef and the second author expressing the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler…
By exploring the consequences of the triviality of the monodromy group for a class of surfaces of which the mixed Hodge structure is pure, we extend results of Miyanishi and Sugie, Dimca, Zaidenberg and Kaliman.
Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on…
We develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetry groups. For polynomials with isolated critical points, the…
We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like…
In this paper we study the influences of the base points of cubic pencils on the Mordell-Weil groups. Specifically, we investigate and classify the cubic pencils with 8, 7 and 6 base points in general position, and give some applications.
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…
We show that two automorphisms of an affine surface with dynamical degree strictly larger than 1 share a Zariski dense set of periodic points if and only if they have the same periodic points. We construct canonical heights for these…
Extending the notion of monodromies associated with open books of $3$-manifolds, we consider monodromies for all incompressible surfaces in $3$-manifolds as partial self-maps of the arc set of the surfaces. We use them to develop a…
Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole…
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their fundamental classes, in terms of Parseval-Rayleigh…
We study irrational pencils with isolated critical points on compact aspherical complex manifolds. We prove that if the set of critical points is nonempty, the homology of the kernel of the morphism induced by the pencil on fundamental…
We show that the coefficients of the characteristic polynomial of a central hyperplane arrangement $\mathcal A$, coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to $\mathcal A$. As a…
We compare different constructions of mirrors of del Pezzo surfaces, focusing on degree $d \leq 3$. In particular, we extract Lefschetz fibrations, with associated exceptional collections, from the mirrors obtained via the Hori-Vafa and…
A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real function singularities, and/or with the Picard--Lefschetz…
We say a mirror pair of Calabi-Yau varieties exhibits strong arithmetic mirror symmetry if the number of points on each variety over a finite field is equivalent, modulo the order of that field. We search for strong mirror symmetry in…
We study the Tannakian properties of the category of perverse sheaves on elliptic curves endowed with the convolution product. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka…