Related papers: Severi Degrees in Cogenus 4

For a homogeneous polynomial of $n$ variables, we present a new method to compute the roots of Bernstein-Sato polynomial supported at the origin, assuming that general hyperplane sections of the associated projective hypersurface have at…

We prove asymptotic estimates for the growth in the degree of the Hodge locus in terms of arithmetic properties of the integral vectors that define it. Our methods are general and apply to most variations of Hodge structures for which the…

Let F denote a homogeneous degree 4 polynomial in 3 variables, and let s be an integer between 1 and 5. We would like to know if F can be written as a sum of fourth powers of s linear forms (or a degeneration). We determine necessary and…

We study a question with connections to linear algebra, real algebraic geometry, combinatorics, and complex analysis. Let $p(x,y)$ be a polynomial of degree $d$ with $N$ positive coefficients and no negative coefficients, such that $p=1$…

We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n \times n$ alternating…

We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories with group actions and categories with graded hom spaces. We…

Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in P3 of degree d >=5. We show, along the same lines, boundedness of families of curves of small enough genera on general…

In this article, we compute $\delta$-invariant of Du Val del Pezzo surfaces of degree $3$.

In this paper we investigate the class of the connected graded algebras which are finitely generated in degree 1, which are finitely presented with relations of degrees greater or equal to 2 and which are of finite global dimension D and…

We consider the space of smooth gradient expanding Ricci soliton structures on $S^1 \times \mathbb{R}^3$ and $S^2 \times \mathbb{R}^2$ which are invariant under the action of $\text{SO}(3) \times \text{SO}(2)$. In the case of each topology,…

A tight map is a map with some of its vertices marked, such that every vertex of degree $1$ is marked. We give an explicit formula for the number $N_{0,n}(d_1,\ldots,d_n)$ of planar tight maps with $n$ labeled faces of prescribed degrees…

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…

The moduli space of degree $d$ morphisms on $\mathbb{P}^1$ has received much study. McMullen showed that, except for certain families of Latt\`es maps, there is a finite-to-one correspondence (over $\mathbb{C}$) between classes of morphisms…

A general method of computing cohomology groups of the space of nonsingular algebraic hypersurfaces of degree $d$ in $CP^n$ is described. Using this method, rational cohomology groups of such spaces with $n=2, d \le 4$ and $n=3=d$ are…

Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous definition of algebraic differential equations on the complex projective space $P^n$. For an algebraic subvariety $S \subseteq P^n$, we present an explicit formula…

Let G be a simple graph without isolated vertices. For a vertex i in G, the degree d_i is the number of vertices adjacent to i and the average 2-degree m_i is the mean of the degrees of the vertices which are adjacent to i. The sequence of…

The purpose of this work is to present the derivation and an estimate of the degrees of the best approximation based on convex, coconvex and unconstrained polynomials, and discuss some applications. We simplify the term convex and coconvex…

Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite…

Nikol'skii inequalities for various sets of functions, domains and weights will be discussed. Much of the work is dedicated to the class of algebraic polynomials of total degree $n$ on a bounded convex domain $D$. That is, we study…

We study a spectral problem related to the finite-dimensional characters of the groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$, which form the classical series $C$, $B$, and $D$, respectively. The irreducible characters of these three series are…