58 citations · 399 across the 82 of their papers we have counts for
15 papers · 1 filter
Unexpected hypersurfaces and their consequences: A Survey
Brian Harbourne, Juan Migliore, Uwe Nagel
The notion of an unexpected curve in the plane was introduced in 2018, and was quickly generalized in several directions in a flurry of mathematical activity by many authors. In th…
On the Weak Lefschetz Property for height four equigenerated complete intersections
Mats Boij, Juan Migliore, Rosa M. Miró-Roig +1
We consider the conjecture that all artinian height 4 complete intersections of forms of the same degree have the Weak Lefschetz Property (WLP). We translate this problem to on…
Schemes supported on the singular locus of a hyperplane arrangement in
J. Migliore, U. Nagel, H. Schenck
We introduce the use of liaison addition to the study of hyperplane arrangements. For an arrangement, , of hyperplanes in , is free if i…
Unexpected hypersurfaces and where to find them
B. Harbourne, J. Migliore, U. Nagel +1
In a recent paper by Cook, et al., which introduced the concept of unexpected plane curves, the focus was on understanding the geometry of the curves themselves. Here we expand the…
Segre's Regularity Bound for Fat Point Schemes
Uwe Nagel, Bill Trok
Motivated by questions in interpolation theory and on linear systems of rational varieties, one is interested in upper bounds for the Castelnuovo-Mumford regularity of arbitrary su…
Resurgences for ideals of special point configurations in coming from hyperplane arrangements
Marcin Dumnicki, Brian Harbourne, Uwe Nagel +3
Symbolic powers of ideals have attracted interest in commutative algebra and algebraic geometry for many years, with a notable recent focus on containment relations between symboli…