47 citations · 309 across the 61 of their papers we have counts for
76 papers · 1 filter
Suciu's Conjecture on hyperplane arrangements
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
We prove that the resonance of any hyperplane arrangement is separable. Using the main result from arXiv:2512.10160 this proves Suciu's conjecture on the fundamental group of every…
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.…
Szegő kernels and Scorza quartics on the moduli space of spin curves
Gavril Farkas, Elham Izadi
We describe an extension at the level of the moduli space of stable spin curves of genus g of the map associating to an ineffective spin structure its Scorza curve (equivalently, t…
Irrational components of the Hilbert scheme of points
Gavril Farkas, Rahul Pandharipande, Alessio Sammartano
We construct irrational irreducible components of the Hilbert scheme of points of affine n-dimensional space, for n at least 12. We start with irrational components of the Hilbert…
The uniruledness of the Prym moduli space of genus 9
Gavril Farkas, Alessandro Verra
We show that the moduli space R_9 of Prym curves of genus 9 is uniruled. This is the largest genus g for which R_g has negative Kodaira dimension.
Difference varieties and the Green-Lazarsfeld Secant Conjecture
Gavril Farkas
The Green-Lazarsfeld Secant Conjecture is a generalization of Green's Conjecture on syzygies of canonical curves to the cases of arbitrary line bundles. We establish the Green-Laza…
Reduced resonance schemes and Chen ranks
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric contexts. We discuss their scheme structure in a gen…
Generalized De Jonquieres divisors on generic curves
Gavril Farkas
The classical De Jonquieres and MacDonald formulas describe the virtual number of divisors with prescribed multiplicities in a linear system on an algebraic curve. We establish an…
The minimal resolution property for points on general curves
Gavril Farkas, Eric Larson
We present an essentially complete solution to the Minimal Resolution Conjecture for general curves, determining the shape of the minimal resolution of general sets of points on a…
Koszul modules with vanishing resonance in algebraic geometry
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace in the second wedge product of a…
The non-abelian Brill-Noether divisor on and the Kodaira dimension of
Gavril Farkas, Dave Jensen, Sam Payne
The paper is devoted to highlighting several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the…
Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6
Valery Alexeev, Ron Donagi, Gavril Farkas +2
In previous work we showed that the Hurwitz space of W(E_6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A_6 of principa…
Linear series on general curves with prescribed incidence conditions
Gavril Farkas, Carl Lian
Using degeneration and Schubert calculus, we consider the problem of computing the number of linear series of given degree and dimension on a general curve of genus sat…
On the Kodaira dimension of Hurwitz spaces
Gavril Farkas, Scott Mullane
We show that the canonical bundle of the Hurwitz stack classifying covers of genus g>1 and degree k>2 of the projective line is big. We show that all coarse moduli spaces of trigon…
On the Kodaira dimension of the moduli space of curves of genus 16
Gavril Farkas, Alessandro Verra
We show that the moduli space of curves of genus 16 is NOT of general type.
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…
The unirationality of the moduli space of K3 surfaces of genus 22
Gavril Farkas, Alessandro Verra
Using the connection discovered by Hassett between the Noether-Lefschetz moduli space of special cubic fourfolds of discriminant 42 and the moduli space F_{22} of polarized K3 surf…
Alternating Catalan numbers and curves with triple ramification
Gavril Farkas, Riccardo Moschetti, Juan Carlos Naranjo +1
It is known that the monodromy group of each cover of a general curve of genus g>3 equals either the symmetric or the alternating group. The classical Catalan numbers count the min…
Koszul modules and Green's conjecture
Marian Aprodu, Gavril Farkas, Stefan Papadima +2
We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green's conjecture for every g-cuspidal rational curve over an algebraically closed field…
Effective divisors on Hurwitz spaces
Gavril Farkas
We prove the effectiveness of the canonical bundle of several Hurwitz spaces of degree k covers of the projective line from curves of genus 13<g<20.