Related papers: Nonnegativity certificates on real algebraic surfa…

We prove a closed formula expressing any multiplicative characteristic class evaluated on the tangent bundle of the Hilbert schemes of points on a non-compact simply-connected surface. As a corollary, we deduce a closed formula for the…

This paper reviews known results on the rigid isotopy classification of plane curves of degree $m\leq6$ and curves of small degrees on quadrics. The paper's study completes the rigid isotopy classification of nonsingular real algebraic…

The invariance of the Welschinger numbers for real unnodal Del Pezzo surfaces, which we used for the enumeration of real rational curves on real toric Del Pezzo surfaces (see math.AG/0303378 and IMRN 49 (2003), 2639-2653), follows from…

In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame…

We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincar\'e from dimension two to dimension…

We obtain a sharp bound on the degree of a globally generated vector bundle over a reduced irreducible projective variety defined over an algebraically closed field of characteristic zero. As an application, we obtain a Del Pezzo-Bertini…

Circuit polynomials are a certificate of nonnegativity for real polynomials, which can be derived via a generalization of the classical inequality of arithmetic and geometric means. In this article, we show that similarly nonnegativity of…

We give a characterization of all del Pezzo surfaces of degree 6 over an arbitrary field $F$. A surface is determined by a pair of separable algebras. These algebras are used to compute the Quillen $K$-theory of the surface. As a…

In this work, we obtain the first upper bound on the multiplicity of Laplacian eigenvalues for negatively curved surfaces which is sublinear in the genus g. Our proof relies on a trace argument for the heat kernel, and on the idea of…

A well-known result of Murray Marshall states that every $f \in \mathbb{R} [X,Y]$ non-negative on the strip $[0,1] \times \mathbb{R}$ can be written as $f= \sigma_0 + \sigma_1 X(1-X)$ with $\sigma_0, \sigma_1$ sums of squares in $\mathbb{R}…

We describe how previously known methods for determining the number of decimation classes of density $\delta$ binary vectors can be extended to nonnegative integer vectors, where the vectors are indexed by a finite abelian group $G$ of size…

We study Le Potier's strange duality on del Pezzo surfaces using quot schemes to construct independent sections of theta line bundles on moduli spaces of sheaves, one of which is the Hilbert scheme of n points. For n at most 7, we use…

We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration…

We classify del Pezzo non-commutative surfaces that are finite over their centres and have no worse than canonical singularities. Using the minimal model program, we introduce the minimal model of such surfaces. We first classify the…

Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative matrices…

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete…

On del Pezzo surfaces, we study effective ample $\mathbb{R}$-divisors such that the complements of their supports are isomorphic to $\mathbb{A}^1$-bundles over smooth affine curves.

We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling,…

We consider rational surfaces $Z$ defined by divisorial valuations $\nu$ of Hirzebruch surfaces. We introduce the concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice local and…