" A detailed algebraic-geometric background is presented for the tropical ap proach to
enumeration of singular curves on toric surfaces, which consists of reducing the …

We prove that there exists a> 0 such that for any integer d> 2 and any topological types
S_1,..., S_n of plane curve singularities, satisfying $\mu (S_1)+...+\mu (S_n)\leq ad^ 2 …

We suggest an approach to construction of algebraic hypersurfaces with given collection of
singular points and polynomials with given collection of critical points. The approach is …

arXiv:math/0205271v2 [math.AG] 16 Mar 2010 Page 1 arXiv:math/0205271v2 [math.AG] 16
Mar 2010 ON LINEAR SYSTEMS OF CURVES ON RATIONAL SCROLLS ANTONIO LAFACE …

1. Introduction. The main objective of this paper is to propose a method for constructing new
ample divisors on rational surfaces by gluing two given ones. Recall that a divisor D on an …

A detailed algebraic-geometric background is presented for the tropical approach to
enumeration of singular curves on toric surfaces, which consists of reducing the …

(2) Given a classification of singular points of planar vector fields, how many singular points
of each type can a vector field of degree d in R2 have? Our approach to these problems …

Let $\mathbb P^ 2_r $ be the projective plane blown up at $ r $ generic points. Denote by $
E_0, E_1,\ldots, E_r $ the strict transform of a generic straight line on $\mathbb P^ 2$ and …

We study families V of curves in P^ 2 of degree d having exactly r singular points of given
topological or analytic types. We derive new sufficient conditions for V to be T-smooth …

By means of the Viro method of gluing real polynomials, we construct polynomials with
prescribed collections of critical points. Using this technique, we solve the problem on the …