Related papers: Monodromy of general hypersurfaces

We prove that every polytope described by algebraic coordinates is the face of a projectively unique polytope. This provides a universality property for projectively unique polytopes. Using a closely related result of Below, we construct a…

We investigate monodromy groups arising in enumerative geometry, with a particular focus on how these groups are influenced by prescribed symmetries. To study these phenomena effectively, we work in the framework of moduli stacks rather…

Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field $\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge…

In this paper we obtain an explicit formula for the number of curves in a compact complex surface $X$ (passing through the right number of generic points), that has up to one node and one singularity of codimension $k$, provided the total…

We prove that the monodromy group of the inflection points of plane curves of degree $d$ is the symmetric group $\mathbb S_{3d(d-2)}$ for $d\geq 4$ and in the case $d=3$ this group is the group of the projective transformations of $\mathbb…

We show that for every smooth generic projective hypersurface $X\subset\mathbb P^{n+1}$, there exists a proper subvariety $Y\subsetneq X$ such that $\operatorname{codim}_X Y\ge 2$ and for every non constant holomorphic entire map…

We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…

In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

Let S be a complex smooth projective surface and L be a line bundle on S. For any given collection of isolated topological or analytic singularity types, we show the number of curves in the linear system |L| with prescribed singularities is…

The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…

We extend the notion of hyperuniformity to the projective spaces $\mathbb{RP}^{d-1}$, $\mathbb{CP}^{d-1}$, $\mathbb{HP}^{d-1}$, and $\mathbb{OP}^2$. We show that hyperuniformity implies uniform distribution and present examples of…

We obtain a sharp characterization of the Euclidean ball among all convex bodies K whose boundary has a pointwise k-th mean curvature not smaller than a geometric constant at almost all normal points. This geometric constant depends only on…

Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…

In this paper, we prove the following version of the famous Bernstein's theorem: Let $X\subset \mathbb R^{n+k}$ be a closed and connected set with Hausdorff dimension $n$. Assume that $X$ satisfies the monotonicity formula at $p\in X$.…

Let $X$ be a projective hypersurface that is not a cone. The symmetrizer group of $X$ is an algebraic group parametrizing hypersurfaces whose Jacobian ideal coincides with that of $X$. We show that if the locus of points in $X$ with…

We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…

The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the…

We establish a general `gluing theorem', which states roughly that if two nondegenerate constant mean curvature surfaces are juxtaposed, so that their tangent planes are parallel and very close to one another, but oppositely oriented, then…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…