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Caporaso and Harris derive recursive formulas counting nodal plane
curves of degree d and geometric genus g in the plane (through the appropriate number of xed
general points). We rephrase their ar...
Computing the Singularities of Rational Surfaces
Singularities of Rational Surfaces Algebraic Geometry
2011/9/21
Abstract: Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $...
Hyperelliptic $d$-osculating covers and rational surfaces
Hyperelliptic $d$-osculating covers rational surfaces
2010/11/19
Let $\mathbb{P}^1$ and $(X,q)$ denote, respectively, the projective line and a fixed elliptic curve marked at its origin, both defined over an algebraically closed field $\mathbb{K}$ of arbitrary cha...
The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle ...