9 papers
Enumerative geometry of surfaces
Thomas Dedieu
The aim of these notes is to explain various enumerative results about surfaces without assuming familiarity with Gromov--Witten theory. The enumerative results in question ar…
Generalized weight properties of resultants and discriminants, and applications to projective enumerative geometry
Laurent Busé, Thomas Dedieu
The goal of this text is to understand and prove a formula stated by Salmon, which gives the first terms of some Taylor expansion of the discriminant of a plane algebraic curve. Sa…
Some classical formulæ for curves and surfaces
Thomas Dedieu
The goal of this text is to present the computation by Salmon, in the second half of the XIXth century, of various numbers enumerating planes with a prescribed tangency pattern wit…
Two lectures on the enumeration of curves by means of floor diagrams
Thomas Dedieu
We discuss, following Mikhalkin, Brugallé, and many others, the counting of curves on toric surfaces with prescribed genus, Newton polygon, and intersection pattern with the toric…
Node polynomials for curves on surfaces
Thomas Dedieu
This text is a presentation of a set of formulae, first found by Vainsencher (for ) and shortly after improved by Kleiman and Piene, counting -nodal curves in a compl…
The Caporaso-Harris-Ran degeneration principle: proof and applications
Francesco Bastianelli, Ciro Ciliberto, Thomas Dedieu +3
Severi varieties are the parameter spaces for curves with prescribed homology class and genus on a smooth surface. We describe their limits along degenerations of surfaces, with a…