Related papers: On modular properties of odd theta-characteristics

The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and analytic objects. In this paper, we perform a new approach…

It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and…

Let $X$ be a germ of real analytic vector field at $({\mathbb R}^{2},0)$ with an algebracally isolated singularity. We say that $X$ is a topological generalized curve if there are no topological saddle-nodes in its reduction of…

In this work we consider constructions of genus three curves $X$ such that $\mathrm{End}(\mathrm{Jac}(X)) \otimes Q$ contains the totally real cubic number field $Q(\zeta _ 7 + \overline{\zeta}_7)$. We construct explicit two-dimensional…

A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises from this definition. Many plausible results follow from this…

Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets…

Let $\X$ be an irreducible, smooth, projective curve of genus $g \geq 2$ defined over the complex field $\C.$ Then there is a covering $\pi: \X \longrightarrow \P^1,$ where $\P^1$ denotes the projective line. The problem of expressing…

Let $Y$ be a generic link of a subvariety $X$ of a nonsingular variety $A$. We give a description of the Grauert-Riemenschneider canonical sheaf of $Y$ in terms of the multiplier ideal sheaves associated to $X$ and use it to study the…

A plane curve is called strange if its tangent line at any smooth point passes through a fixed point, called the strange point. In this paper, we study $\mathbb{A}^1$-curves on the complement of a rational strange curve of degree $p$ in…

We define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…

A T-variety is an algebraic variety X with an effective regular action of an algebraic torus T. Altmann and Hausen gave a combinatorial description of an affine T-variety X by means of polyhedral divisors. In this paper we compute the…

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…

We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all…

For a curve $X$ of genus $>1$ defined over a finite field, we present a criterion which allows us to state the non existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the…

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…

We introduce two generalizations of Newton-non-degenerate (Nnd) singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called topologically Newton-non-degenerate (tNnd) if the local embedded topological…

In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the rational cohomology of moduli spaces of cyclic covers of curves where the genus of…

The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issues given therein and providing solutions to problems raised…

We classify all possible limits of families of translates of a fixed, arbitrary complex plane curve. We do this by giving a set-theoretic description of the projective normal cone (PNC) of the base scheme of a natural rational map,…

We are concerned with the question of determining the set $C(\mathbb{Q})$, where $C$ is a curve defined by an equation of the form $y^q=f(x)$, where $q$ is an odd prime and $f$ is a polynomial defined over $\mathbb{Q}$. This question can…