40 citations · 297 across the 38 of their papers we have counts for
41 papers
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…
Linear sections of Grassmannians and resonance of vector bundles
Marian Aprodu, Călin Spiridon
This work revolves around the question of whether a given resonance variety is associated with a vector bundle. We show the existence of a family of natural morphisms on a stratifi…
The second syzygy schemes of curves of large degree
Marian Aprodu, Andrea Bruno, Edoardo Sernesi
The present paper is a natural continuation of a previous work where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second…
Resonance, syzygies, and rank- Ulrich bundles on the del Pezzo threefold
Marian Aprodu, Yeongrak Kim
We investigate a geometric criterion for a smooth curve of genus and degree to be described as the zero locus of sections in an Ulrich bundle of rank on a del Pez…
Sections of K3 surfaces with Picard number two and Mercat's conjecture
Marian Aprodu, Laura Filimon
Farkas and Ortega found counterexamples to Mercat's conjecture by restricting to a hyperplane section some suitable rank-two vector bundles on a surface whose Picard group…
Higher resonance schemes and Koszul modules of simplicial complexes
Marian Aprodu, Gavril Farkas, Claudiu Raicu +2
Each connected graded, graded-commutative algebra of finite type over a field of characteristic zero defines a complex of finitely generated, graded modules over a symm…