Syzygies, Hurwitz spaces and Ulrich sheaves

• Applicant: Professor Dr. Gavril Farkas
• Subject Area: Mathematics
• Term: from 2013 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 239456820

The Hurwitz space is the parameter space of degree k ramified coverings of the projective line by smooth curves of genus g. Via the Riemann existence theorem, every curve of genus g appears in this way, for a suitable choice of k. We propose to use syzygy methods to determine asymptotically the geometric nature (Kodaira dimension) of this space and study its singularities. Our methods should completely describe the resolution of a general k-gonal curve of genus g and lead to a full solution of a well-known conjecture of Green-Lazarsfeld concerning the minimal resolution of the coordinate ring associated to a non-special line bundle on a curve. Several generalizations of Green’s conjecture are proposed and will be tested with the help of computer algebra.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• International Connection: Italy, Romania
• Participating Persons: Professor Dr. Marian Aprodu; Professor Dr. Alessandro Verra