6 papers
The unirationality of and moduli spaces of pointed spin curves
Gavril Farkas, Alessandro Verra
We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known. This is achieved by realizing birationally t…
Syzygies and Koszul modules in geometry
Gavril Farkas
We describe the progress in the last 10 years related to Koszul modules and syzygies of algebraic varieties. Topics discussed include the general theory of Koszul modules and reson…
The effective Chen ranks conjecture
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
Koszul modules and their associated resonance schemes are objects appearing in a variety of contexts in algebraic geometry, topology, and combinatorics. We present a proof of an ef…
Secant loci on moduli of Prym varieties
Gavril Farkas, Margherita Lelli-Chiesa
We present a Prym analogue of Lazarsfeld's result that curves on general polarized K3 surfaces verify the Brill-Noether Theorem, or equivalently, that their canonical embedding has…
Hurwitz-Brill-Noether theory via K3 surfaces and stability conditions
Gavril Farkas, Soheyla Feyzbakhsh, Andrés Rojas
We develop a novel approach to the Brill-Noether theory of curves endowed with a degree k cover of the projective line via Bridgeland stability conditions on elliptic K3 surfaces.…
The Kodaira dimensions of and
Gavril Farkas, David Jensen, Sam Payne
We prove that the moduli spaces of curves of genus 22 and 23 are of general type. To do this, we calculate certain virtual divisor classes of small slope associated to linear serie…