EAGER

Node of the University of Roma Tor Vergata

Coordinator: Ciro Ciliberto

• Introduction and subnodes
• Expertise
• Contribution to projects
• Links with other nodes of EAGER network
• Annual reports (2000/2001)
• Some web links

EAGER is an European network based on a research project in Algebraic Geometry. The project includes most of the European researchers active in the field. EAGER stimulates mobility of young researchers inside the European Community. Detailed information about the structure of the network can be found in the EAGER web site.

The EAGER node of Rome collects about 100 members active in research from the following Italian Universities: Bari, Catania, Cosenza, Ferrara, Firenze, L'Aquila, Napoli, Pavia, Perugia, Pisa, Roma La Sapienza, Roma Tor Vergata and Roma 3.

The node is organized in subnodes in the following way:

1. subnode of Bari, local coordinator: M. Boratynski;
2. subnode of Catania, local coordinator: A. Ragusa, other main researchers: R. Strano;
3. subnode of Cosenza, local coordinator: P. Oliverio;
4. subnode of Ferrara, local coordinator: Ph. Ellia;
5. subnode of Firenze, local coordinator: G. Ottaviani, other main researchers: V. Ancona;
6. subnode of L'Aquila, local coordinator: A. Biancofiore;
7. subnode of Napoli, local coordinator: F. Orecchia;
8. subnode of Pavia, local coordinator P. Pirola, other main researchers: M. Cornalba, B. Van Geemen;
9. subnode of Perugia, local coordinator: A. Lorenzini;
10. subnode of Pisa, local coordinator: R. Pardini, other main researchers: E. Arbarello, F. Bardelli, M. Salvetti;
11. subnode of Roma La Sapienza, local coordinator: R. Salvati Manni, other main researchers: E. Arbarello, K. O'Grady, M. Manetti;
12. subnode of Roma Tor Vergata, local coordinator: C. Ciliberto, other main researchers: G. Pareschi, R. Schoof;
13. subnode of Roma 3, local coordinator: A. Verra, other main researchers: L. Caporaso, L. Chiantini, A. Lopez, E. Sernesi.

The coordinator of the node is Ciro Ciliberto (University of Roma Tor Vergata).

Expertise:

1. Algebraic curves and their moduli spaces. The geometry and the cohomology of the moduli space of curves and its enumerative geometry. Hilbert schemes, the geometry of the theta divisor of a jacobian and of a Prym variety, moduli of vector bundles on curves, their Betti numbers and their cohomology, generalized Brill-Noether theory and generalized theta functions.
2. Algebraic surfaces. Canonical and pluricanonical mappings for surfaces of general type. Families of singular curves on surfaces. Special surfaces and related enumerative questions using degeneration techniques. Moduli spaces for sheaves on projective surfaces, their topology, their stable cohomology, their Chow rings.
3. Special varieties and related algebraic and computational problems. Moduli spaces of instanton bundles, their cohomology and local equations. Quantum cohomology of special varieties and of projective bundles. Computer programs for computing cohomology and local equations of moduli spaces of instanton bundles.
4. Abelian varieties. The Schottky problem. Subvarieties on a general abelian variety. Singularities of theta divisors. Abelian varieties as Prym-Tyurin varieties. Families of jacobians with non-trivial endomorphisms. Modular forms techniques. Projective embeddings of abelian varieties. Elliptic curves and abelian varieties and related arithmetical and computational problems.
5. Higher dimensional varieties. Deformation theories and formal moduli spaces. Fano varieties and Calaby-Yau varieties. Mori contractions in higher dimensions. Local and global Hodge theory. Projective embeddings of varieties.

Contribution to project:

• By joint reseach with various teams active in the network EAGER.
• By training of joung researchers which will be visiting several subnodes (Firenze, Pavia, Pisa, Roma Tor Vergata, Roma Tre).
• By organizing joint activities, like the following:
  1. Workshop on Algebraic Surfaces, organized in collaboration with the Italian MURST project Algebraic geometry, Furore (Salerno, Italy), 39/9-3/10/1999, organizers: C. Ciliberto, M. Manetti, invited speakers (partial list): F. Catanese, L. Goettsche, R. Miranda, Ch. Ranestad, M. Reid, M. Teicher, C. Voisin.
  2. the annual school PRAGMATIC in Catania;
  3. Italy-Israeli meeting on Algebraic Geometry, organized by C. Ciliberto and M. Teicher. Third edition: Application of Algebraic Geometry to Coding Theory, Phisics and Computation, Eilat (Israel), 25/2-1/3/2001;
  4. Workshop on Zero-dimensional schemes and applications, organized in collaboration with the Italian MURST project Algebraic geometry, Napoli, 9/2-12/2/2000;
  5. Summer school in Ravello (time and topic to be decided);
  6. Workshop on Deformation theory, formal moduli spaces, mirror symmetry and Virasoro's conjecture, Cortona (time to be decided), organized by the subnode of Pisa;
  7. Workshop VBAC,organized by the subnode of Roma Tre, 11-16/9/2001.

Existing links (referring to the above listed scientific interests):

• Amsterdam (a, c, d);
• Barcelona (b, c, d);
• Bar Ilan (b, c, d, e);
• Bayreuth (a, b, c, d);
• Durham (a);
• Erlangen (d);
• Hannover (a, b, c);
• Göttingen (b, d, e);
• Hannover (a, b, c, d, e);
• Kaiserslautern (c);
• Lisbon (b);
• Liverpool (a);
• Madrid (c);
• Orsay (a, b, c, d, e);
• Oslo (c);
• Paris (a, b);
• Saarbrucken (c);
• Warsaw (c, e);
• Warwick (b);
• Zürich (b, c, d, e).

You may find here the financial report and here a pdf file with the scientific report of this node.

Some Web links:

• node of Nice and Orsay;
• department of Mathematics;
• university of Roma "Tor Vergata".

For more Web links, please refer to EAGER web site.