T. Dedieu

activity

20072026

most citedWahl maps and extensions of canonical curves and K3 surfaces

15 citations · 76 across the 27 of their papers we have counts for

collaborators

28 papers

math.AG2026

Enumerative geometry of $K 3$ surfaces

Thomas Dedieu

The aim of these notes is to explain various enumerative results about $K 3$ surfaces without assuming familiarity with Gromov--Witten theory. The enumerative results in question ar…

math.AG2025

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…

math.AG2025

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…

math.AG2025

Node polynomials for curves on surfaces

Thomas Dedieu

This text is a presentation of a set of formulae, first found by Vainsencher (for $δ \leq 6$ ) and shortly after improved by Kleiman and Piene, counting $δ$ -nodal curves in a complet…

math.AG2025

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…

math.AG2025

On surfaces of high degree with respect to the sectional genus

Ciro Ciliberto, Thomas Dedieu, Margarida Mendes Lopes

We study and classify linearly normal surfaces in $P^{n}$ , of degree $d$ and sectional genus $g$ , such that $d \geq 2 g - 1$ .

math.AG2023★ 2 cited

Extensions of curves with high degree with respect to the genus

Ciro Ciliberto, Thomas Dedieu

We classify linearly normal surfaces $S \subset P^{r + 1}$ of degree $d$ such that $4 g - 4 \leq d \leq 4 g + 4$ , where $g > 1$ is the sectional genus (it is a classical result that…

math.AG2021★ 6 cited

Nonemptiness of Severi varieties on Enriques surfaces

Ciro Ciliberto, Thomas Dedieu, Concettina Galati +1

Let $(S, L)$ be a general polarized Enriques surface, with $L$ not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible $δ$ -n…

math.AG2021★ 2 cited

Severi varieties on blow--ups of the symmetric square of an elliptic curve

Ciro Ciliberto, Thomas Dedieu, Concettina Galati +1

We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are non-empty and smooth o…

math.AG2021

On the automorphisms of Mukai varieties

Thomas Dedieu, Laurent Manivel

Mukai varieties are Fano varieties of Picard number one and coindex three. In genus seven to ten they are linear sections of some special homogeneous varieties. We describe the gen…

math.AG2021★ 4 cited

Deformations and extensions of Gorenstein weighted projective spaces

Thomas Dedieu, Edoardo Sernesi

We study the existence of deformations of all $14$ Gorenstein weighted projective spaces $P$ of dimension $3$ by computing the number of times their general anticanonical d…

math.AG2020★ 7 cited

$K 3$ curves with index $k > 1$

Ciro Ciliberto, Thomas Dedieu

Let $K C_{g}^{k}$ be the moduli stack of pairs $(S, C)$ with $S$ a $K 3$ surface and $C \subset S$ a genus $g$ curve with divisibility $k$ in $Pic (S)$ . In this article…

math.AG2020

Double covers and extensions

Ciro Ciliberto, Thomas Dedieu

In this paper we consider double covers of the projective space in relation with the problem of extensions of varieties, specifically of extensions of canonical curves to $K 3$ surf…

math.AG2019

Comment on: On the irreducibility of the Severi variety of nodal curves in a smooth surface, by E. Ballico

Thomas Dedieu

In this short note, I point out that results of Ballico and Kool--Shende--Thomas together imply that on $K 3$ , Enriques, and Abelian surfaces, if $L$ is a very ample and $(2p_a(L)-2…

math.AG2019★ 3 cited

On the locus of Prym curves where the Prym--canonical map is not an embedding

Ciro Ciliberto, Thomas Dedieu, Concettina Galati +1

We prove that the locus of Prym curves $(C, η)$ of genus $g \geq 5$ for which the Prym-canonical system $∣ ω_{C} (η) ∣$ is base point free but the Prym--canonical map is not an embedding…

math.AG2019★ 1 cited

Moduli of curves on Enriques surfaces

Ciro Ciliberto, Thomas Dedieu, Concettina Galati +1

We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym…

math.AG2018

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…

math.AG2018★ 8 cited

A note on Severi varieties of nodal curves on Enriques surfaces

C. Ciliberto, T. Dedieu, C. Galati +1

Let $∣ L ∣$ be a linear system on a smooth complex Enriques surface $S$ whose general member is a smooth and irreducible curve of genus $p$ , with $L^{2} > 0$ , and let $V_{∣ L ∣, δ} (S)$ b…

math.AG2018★ 11 cited

Irreducible unirational and uniruled components of moduli spaces of polarized Enriques surfaces

Ciro Ciliberto, Thomas Dedieu, Concettina Galati +1

We give an explicit description of the irreducible components of the moduli spaces of polarized Enriques surfaces in terms of decompositions of the polarization as an effective sum…

math.AG2018★ 1 cited

On the irreducibility of Severi varieties on K3 surfaces

Ciro Ciliberto, Thomas Dedieu

Let $(S, L)$ be a polarized $K 3$ surface of genus $p ⩾ 11$ such that $Pic (S) = Z [L]$ , and $δ$ a non-negative integer. We prove that if $p ⩾ 4 δ - 3$ , the…

math.AG2018★ 15 cited

Wahl maps and extensions of canonical curves and K3 surfaces

Ciro Ciliberto, Thomas Dedieu, Edoardo Sernesi

Let $C$ be a smooth projective curve of genus $g \geq 11$ , non-tetragonal, considered in its canonical embedding in $P^{g - 1}$ . We prove that $C$ is a linear section of an…

math.AG2015★ 11 cited

Numerical characterisation of quadrics

Thomas Dedieu, Andreas Höring

Let X be a Fano manifold such that every rational curve in X has anticanonical degree at least the dimension of X. We prove that X is a projective space or a quadric.

math.AG2014

Equigeneric and equisingular families of curves on surfaces

Thomas Dedieu, Edoardo Sernesi

We investigate the following question: let $C$ be an integral curve contained in a smooth complex algebraic surface $X$ ; is it possible to deform $C$ in $X$ into a nodal curve whil…

math.AG2013

Limits of pluri-tangent planes to quartic surfaces

Ciro Ciliberto, Thomas Dedieu

We describe, for various degenerations $S \to Δ$ of quartic $K 3$ surfaces over the complex unit disk (e.g., to the union of four general planes, and to a general Kummer surface), th…

Enumerative geometry of K3 surfaces

Some classical formulæ for curves and surfaces

Two lectures on the enumeration of curves by means of floor diagrams

Node polynomials for curves on surfaces

The Caporaso-Harris-Ran degeneration principle: proof and applications

On surfaces of high degree with respect to the sectional genus

Extensions of curves with high degree with respect to the genus

Nonemptiness of Severi varieties on Enriques surfaces

Severi varieties on blow--ups of the symmetric square of an elliptic curve

On the automorphisms of Mukai varieties

Deformations and extensions of Gorenstein weighted projective spaces

K3 curves with index k>1

Double covers and extensions

Comment on: On the irreducibility of the Severi variety of nodal curves in a smooth surface, by E. Ballico

On the locus of Prym curves where the Prym--canonical map is not an embedding

Moduli of curves on Enriques surfaces

Generalized weight properties of resultants and discriminants, and applications to projective enumerative geometry

A note on Severi varieties of nodal curves on Enriques surfaces

Irreducible unirational and uniruled components of moduli spaces of polarized Enriques surfaces

On the irreducibility of Severi varieties on K3 surfaces

Wahl maps and extensions of canonical curves and K3 surfaces

Numerical characterisation of quadrics

Equigeneric and equisingular families of curves on surfaces

Limits of pluri-tangent planes to quartic surfaces

Enumerative geometry of $K 3$ surfaces

$K 3$ curves with index $k > 1$