(announcement, speakers and lectures, bibliography)

1) Announcement  (from June 2014)

"Dear All,

In July, at IM PAN, there will be a seminar devoted to reading together a series of papers on Jacobians, Prym varieties, other abelian varieties and on Picard sheaves. We want to study these varieties with the help of some properties of vector bundles on them. An example of a result in this direction is the following theorem of Debarre: ``On a Jacobian there is a vector bundle of rank equal to its dimension, and a section of the bundle which vanishes precisely at a single point''. Debarre speculates that, appropriately formulated, this property may serve to characterize Jacobians, giving an alternative solution to the Schottky problem.

We assume basic algebraic geometry and basic results on abelian varieties.

We meet on Fridays:  4.07., 11.07., 18.07., 25.07. and 1.08. at:

10:30-12:00 and 13:00-14:30  in  Room 408.

See you at this summer seminar of IMPANGA,

Jesse Kass and Piotr Pragacz"

2) Speakers and their lectures

Speakers: Paweł Borówka (IM UJ), Jesse Kass (South Carolina), Piotr Pragacz (IM PAN)

P. Borówka lectured on Poincare bundles for abelian varieties, in
particular, for Jacobians. He also described Picard sheaves and
their properties.

J. Kass lectured on
the Fourier-Mukai transform and Mukai's
cohomological computations. He applied them to a study of Picard

P. Pragacz lectured on the work of Debarre on the point property
for abelian varieties. He also described various approaches to
the Schottky problems for Jacobians and Pryms following Beauville.

Moreover, S. Singh (TIFR, IM PAN) made some remarks on  Picard sheaves.

3) Bibligraphy:

E. Arbarello, M. Cornalba, P.A. Griffiths and J. Harris,
Geometry of Algebraic Curves, Volume I,
Springer, Berlin 1985.

A. Beauville,
Prym Varieties and the Schottky Problem,
Invent. Math. 41 (1977), 149--196.

A. Beauville,
Les singularities du diviseur Theta de la jacobienne intermediare de l'hypersurface cubique dans P^4,

A. Beauville,
Varieties de Pryms et jacobiennes intermediares,
Ann. Sci. ENS 40 (1977), 309--391.

A. Beauville, O. Debarre,
Une relation entre deux approaches de probleme de Schottky,
Invent. Math. 86 (1986), 195--207.
A. Beauville, O. Debarre,
Sur le probleme de Schottky pour les varietes de Prym,
Annali della SNS Pisa 14 (1987), 613--623.

C. Birkenhake, H. Lange,
Complex Abelian Varieties,
Springer, Berlin 2004.

A. Collino,
A new proof of the Ran-Matsusaka criterion for Jacobians,
Proc. AMS 92 No.3 (1984), 329--331.

O. Debarre,
Degree of curves in abelian varieties,
Bull. Soc. Math. France 122 (1994), 101--119.

O. Debarre,
The diagonal property for abelian varieties,
Contemporary Mathematics AMS 465 (2008), 45--50.

T. Ekedahl, J-P. Serre,
Exemples de courbes algebriques a jacobienne completement decomposable,
C. R. Acad. Sci. Paris 317 (1993), 509--513.

G. van der Geer, B. Moonen,
Abelian varieties,

P. Griffiths, J. Harris,
Principles of algebraic geometry,
Wiley, New York 1978.

R. Hartshorne,
Algebraic Geometry,
Springer, GTM 52, Berlin 1977.

S. Koizumi,
The ring of algebraic correspondences on a generic curve of genus g,
Nagoya Math. J. 60(1976), 173--180.

H. Lange,
Modulprobleme exzeptioneller abelscher Varetaeten,
Nachrichten der Akademie der Wissenschaften Gottingen (1975) 35--42.

A. C. Lopez Martin, E. Mistretta, D. Sancho Gomez,
A characterization of Jacobians by the existence of Picard bundles,

A. Mattuck,
Symmetric products and Jacobians,
Amer. J. Math. 83 (1961), 189--206.

A. Mattuck,
Picard bundles,
Illinois J. Math. 5 (1961), 550--564.

S. Mukai,
Duality between D(X) and D(^X) with its applications to Picard sheaves,
Nagoya Math. J. 81 (1981), 153--175.

D. Mumford,
Prym varieties I
in: ``Contributions to Analysis'' (V. Ahlfors et al. eds.)
Academic Press, New York (1974), 325--350.

M. S. Narasimhan and S. Ramanan,
Generalised Prym varieties as fixed points,
J. Indian Math. Soc. 39 (19735) 1-19.

G. P. Pirola,
Base number theorem for abelian varieties. An infinitesimal approach,
Math. Ann. 282 (1988), 361--368.

P. Pragacz, V. Srinivas and V. Pati,
Diagonal subschemes and vector bundles,
Pure and Applied Math. Quarterly 4(4) (Special Issue in honor of
J-P. Serre, Part 1 of 2) (2008), 1233--1278.

Z. Ran,
On subvarieties of abelian varieties,
Inv. Math 62 (1881), 459--479.

R. L. E. Schwarzenberger,
Jacobians and symmetric products,
Illinois J. Math. 7 (1963), 257--268.