II Latin American School of Algebraic Geometry and Applications (II ELGA)

La Plage , Cabo Frio, RJ, June, 1 – 12

The goal of this CIMPA research school is to train young mathematicians working in Latin America in some of the most active areas of research in Algebraic Geometry, as well as to promote greater interaction among researchers and students, and to build a network of collaborations.

The first week of the school will consist of 4 mini-courses covering different aspects of Algebraic Geometry, all taught in English. There will be also poster presentations by young researchers and students. The second week will consist of research talks by leading specialists, as well as presentations by young researchers.





Confirmed Speakers

Michela Artebani (Universidad de Concepción, Chile)
About the semiample cone of the symmetric product of a curve

Jérémy Blanc (Universität Basel, Switzerland)
Dynamical Degrees of Birational transformations of projective surfaces

Michel Brion (Institut Fourier, France)
Minimal rational curves on group compactifications

Severino Collier Coutinho (Universidade Federal do Rio de Janeiro, Brazil)
On the construction of minimal involutive varieties

Alicia Dickenstein (Universidad de Buenos Aires, Argentina)
From chemical reaction networks to Descartes’ rule of signs

Eduardo Esteves (IMPA, Brazil)
Limit linear series, a new perspective

Xavier Gómez-Mont (CIMAT, Mexico)
Geometric and Algebraic Jordan Block Structure in Vanishing Cohomology and in the Jacobian Algebra of an Isolated Singularity

Paul Hacking (University of Massachusetts at Amherst, USA)
Theta functions for K3 surfaces

Seyed Hamid Hassanzadeh (Universidade Federal do Rio de Janeiro, Brazil)
On the Geometry of Syzygies of Birational Maps

Abramo Hefez (Universidade Federal Fluminense, Brazil)
The polar curves of plane branches

Sándor Kovács (University of Washington, USA)
Projectivity of the moduli space of stable log-varieties

Diane Maclagan (Warwick University, UK)
Tropical schemes

Amílcar Pacheco (Universidade Federal do Rio de Janeiro, Brazil)
Explicit bound for a conjecture of lang on curves over function fields

Ragni Piene (University of Oslo, Norway)
Higher order self-dual toric varieties

Kristian Ranestad (University of Oslo, Norway)
Power sum presentations of cubic forms, and generalizations

Colleen Robles (Texas A&M University, USA)
Horizontal Schubert varieties

Rubí Rodríguez (Universidad de la Frontera, Chile)
Abelian Varietes and Actions

Jason Starr (Stony Brook University, USA)
Picard Groups of Spaces of Rational Curves in Fano Manifolds

Damiano Testa (Warwick University, UK)
K3 surfaces arising from arithmetic problems

Jenia Tevelev (University of Massachusetts, USA)
The Craighero-Gattazzo surface is simply-connected

Giancarlo Urzúa (Pontificia Universidad Catolica, Chile)
On Chern slopes of simply connected surfaces in any characteristic

Israel Vainsencher (Universidade Federal de Minas Gerais, Brazil)
Holomorphic foliations singular along a positive dimensional subscheme

Mauricio Velasco (Universidad de los Andes, Colombia)
Nonnegativity certificates on real algebraic curves

Organizing Committee

– Carolina Araujo (IMPA, Brazil)
– Cinzia Casagrande (Università di Torino, Italy)
– Ana-Maria Castravet (Ohio State University, USA)
– Stéphane Druel (Institut Fourier, France)
– Antonio Laface (Universidad de Concepción, Chile)

Registered Participants


Scientific Committee

– Lucia Caporaso (Università di Roma Tre, Italy)
– Alicia Dickenstein (Universidad de Buenos Aires, Argentina)
– Eduardo Esteves (IMPA, Brazil)
– Lothar Göttsche (ICTP, Italy)
– Sándor Kovács (University of Washington, USA)

Mini Courses

1st Week – School (June 1-5, 2015)


– Line bundles and divisors, linear equivalence, maps to projective space
– Vector bundles
– Smoothness, tangent and normal bundles
– Coherent sheaf cohomology
– Singular cohomology
– Basic theorems on dimensions of fibers
– Hilbert’s theorem on syzygies
– Genus of a curve
– Elliptic curves
– Intersection numbers on a surface
– Canonical bundle, adjunction formula

Course 1
Curves of low degrees on Fano varieties (Olivier Debarre – ENS, France)

Abstract – Notes

Course 2
Classical and virtual intersection theory (Barbara Fantechi – SISSA, Italy)

Abstract – Notes

Course 3
Equations defining projective varieties (Robert Lazarsfeld – Stony Brook University, USA)

Abstract – Notes

Course 4
Algebraic cycles and birational geometry (Burt Totaro – UCLA, USA)

Abstract – Notes

Poster Session

Tuesday 2nd
(17:30 – 19:00)

Fibrations on general type surfaces
Alejandra Fabiola Huitrado Mora and Margarita Castaneda

On the Milnor number in positive characteristic
João Hélder

Non-degenerate Polar Curves for Plane Branches
Fernando Hernández Iglesias

The Cox rings of smooth projective rational surfaces
Juan Bosco Frias Medina

Irreducible components of the space of holomorphic foliations in CP^n
Fábio Xavier Penna

Nonnegative Reflection-Invariant Polynomials
Jose Gabriel Acevedo Habeych

Presentation by Young Researchers – PYR

1st week

– Thursday 4th (17:30 – 19:00)

Pluri-forms on singular rationally connected surfaces
Wenhao Ou

On the space of conics through two points
Rafael Lucas de Arruda

The generalised Hoppe stability criterion on polycyclic varieties
Henrique Sá Earp

The Kupka set and unfoldings
Ariel Molinuevo

Explicit log Fano structures on blow-ups of projective spaces
Alex Massarenti

Geometry of Tautological Bundles on Hilbert Schemes of Points
David Stapleton

2nd week

– Tuesday 9th (18:10 – 19:10)

Dual families of Calabi-Yau hypersurfaces
Paola Comparin

On the unification of toric mirror constructions
Robin Guilbot

On Stable Quintic Surfaces
Julie Rana

Compactifying the space of smooth quadrics
César Huerta

– Thursday 11th (17:00 – 18:00)

On Kobayashi’s conjecture of K3 surfaces and hyperkahler manifolds-
Ljudmila Kamenova

Tropicalization of singular varieties
Isabel Herrero

Arithmetical rank and cohomological dimension of the determinantal ideals
Maral Mostafazadehfard

Stable limit linear series on singular curves
Pedro Hernandez Rizzo







Registration and Financial Support

Registration for the II ELGA is now closed.

Due to limitations of space in the venue of the school, we can no longer accept registration of participants.

If you are na invited speaker and has not yet registered, please email: elga2015@impa.br .

Those registered graduate students and young researchers from Latin América (except Brazil) can still apply for financial support for travel at UMALCA´s webpage ( Deadline March 1st, 2015 ):



Venue and accomodation cost

Hotel La Plage, Cabo Frio, Brazil

Rates are in Brazilian currency, and include breakfast, lunch and dinner:

Single: R$ 236,00 + 15% per room per day
Double: R$ 360,00 + 15% per room per day
Triple: R$ 470,00 + 15% per room per day


We will provide a bus to take participants from Rio de Janeiro to Cabo Frio on Sunday afternoon, May 31 and June 7, and returning to Rio de Janeiro on Saturday morning, June 6 and 13. Details will be announced later.

Transportation Information

Going to Hotel La Plage – From Rio de Janeiro to Cabo Frio

Sunday – May 31 – Bus list

Sunday – June 7

Back from Cabo Frio to Rio de Janeiro

Saturday – June 6

Saturday – June 13



Postal Address: Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brasil
E-mail: eventos@impa.br