Giuseppe Pareschi

Research Interests:

• My field of research is Algebraic Geometry, especially the geometry of complex projective varieties.
• In recent years, I focused on various aspects of irregular and abelian varieties and the use of the Fourier-Mukai transform for investigating them.  In joint works with Mihnea Popa (University of Illinois at Chicago) I begun a systematic study of algebraic coherent sheaves on abelian and irregular varieties via generic vanishing conditions and local homological methods, with applications to the study of subvarieties of abelian varieties, the Schottky problem and the geometry/topology of irregular varieties.
• Another subject I have been working recently is that of syzygies of projective varieties. Roughly speaking, I study the interaction between  homological properties of the homogeneous ideal of a projectively embedded variety and the intrinsic geometry of the variety.

 CV: cv.pdf