Centro Internazionale per la Ricerca Matematica (CIRM),
                 Istituto Trentino di Cultura

        PRIN 2001 Project "Spazi di Moduli e Teoria di Lie"

          MIUR 2002 PIN Project "Geometria sulle Varietà Algebriche"
 
 

SCHOOL-WORKSHOP
"GEOMETRY OF THE FOURIER MUKAI TRANSFORM"

Levico Terme (Trento, Italy), June 15-20, 2003

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The aim of the school-workshop is to offer an outline of the present state of  research concerning the geometry of the Fourier Mukai transform.  It is the intention of the organizers to put together young researchers  and well-known researchers active in the field and to encourage  informal discussion on current research trends and developments  in the area.

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The following speakers have agreed to give short courses of 5 hours each:

Christopher Hacon (Salt Lake City): "Fourier Mukai Transforms of the Birational Geometry"
Abstract. The purpose of these lectures is to illustrate how the theory of Fourier Mukai transforms, vanishing and generic vanishing theorems can be combined to give surprisingly precise results
in the birational classification of irregular varieties.
Lecture topics
a) A derived category approach to generic vanishing theorems
b) Effective criteria for birational morphisms
c) Effective generation of adjoint linear series
d) Characterization of theta divisors
e) Characterization of abelian varieties

Giuseppe Pareschi (Roma II): "Some applications of the Fourier-Mukai transform on abelian varieties"
Abstract. The Fourier-Mukai transform  provides a very natural way to perform certain cohomological computations with coherent sheaves on abelian
varieties.  For example, the FM point of view supplies a theta group-free treatment of certain classical theorems about  line bundles on abelian
varieties and this allows both considerable improvements and generalizations of such results.  As another example, the FM transform
supplies -- via "global co-gaussian maps" -- a completely algebraic approach to Green-Lazarsfeld's generic vanishing theorem (in strong form)
and (hopefully) to the study of cohomological support loci.
Provisional topics:
(1) Multiplication maps and FM transform.  Criteria for global generation of sheaves on abelian varieties.
(2) Defining equations and syzigies of abelian varieties. Normal generation of semi-homogeneous  vector bundles and applications.
(3) Theta-equations defining certain special subvarieties in jacobians.
(4) Higher order properties of projective embeddings of abelian varieties. Fujita-type results for certain irregular varieties.
(5) Gaussian maps and FM transform.  Higher direct images of Poincare' line bundles. Hopefully some applications.

Alexander Polishchuk (Boston): "Fourier-Mukai Transform, Mirror Symmetry and Noncommutative Geometry"
Abstract. I will talk about connections between the Fourier-Mukai transform and the homological mirror symmetry for tori. I will also consider a version of the Fourier-Mukai for noncommutative tori and its relation to noncommutative mirror symmetry.

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Participants will be lodged at Grand Hotel Bellavista in Levico Terme ( http://www.ghbellavista.com/). The lecture room is inside the Hotel.
Price for an all-in arrangement (i.e. full board accommodation) will be as follows:

- 58 Euro per participant per night in single room,
- 52 Euro per participant per night in double room,
- 65 Euro per participant per night in double room (single use).

A restricted number of grants for financial support of living expenses is available. Interested persons should send the enclosed application form before May 15 to:
    Mr. Augusto Micheletti
    Secretary of CIRM
    Istituto Trentino di Cultura
    I-38050 Povo (Trento)
    Italy.
    michelet@science.unitn.it
    Fax 0039/0461/810629, Phone 0039/0461/881628

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Levico Terme is a small village located about 20 km east from Trento, close to a lake and surrounded by Dolomiti mountains. Geographical and historical information on Trento and the region Trentino can be found at   http://www.unitn.it/trentino/trentino.html  .
Levico is connected to Trento by train and by bus. Trento is connected by train to Verona (92 km), Milano (240 km), Venezia (212 km), where there are international airports.
On the arrival day, we plan to organize a shuttle-bus from Trento Railway Station to the Grand Hotel Bellavista in Levico.
More details on the place of the school and travel information (including train time-table) can be found at
 http://www.science.unitn.it/cirm/travelbella.html
 
 
 

                                                                 Giorgio Bolondi, Rita Pardini, Gian Pietro Pirola
                                                                                     (Scientific Organizers)

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Related link:

 For 2003 CIRM program