The gonality of complete intersection curves

On gonality, scrolls, and canonical models of non-Gorenstein curves

“…As observed in [19], the efforts we make here to charcterize gonality via scrolls, though general, are still incipient. A detailed study of syzygies in the same way of, e.g., [26] or [7] (and references therein), will likely be required; or even adjusting the techniques of the recent [16] (and references therein) to canonical models, and also scrolls as the ambient space.…”

Multiplicative bounds for measures of irrationality on complete intersections

“…, a e ) with 2 ≤ a 1 ≤ • • • ≤ a e is bounded from below by gon(C) ≥ (a 1 − 1)a 2 • • • a e . Further refinements due to Hotchkiss, Lau, and Ullery [10] show that when 4 ≤ a 1 < a 2 ≤ • • • ≤ a e holds, the gonality of the curve C is realized by projection from a suitable linear subspace. In higher dimensions, Stapleton [18] used results about Seshadri constants on hypersurfaces which were due to Ito [11] to give bounds for the The author's research was partially supported by an NSF postdoctoral fellowship, DMS-2103099.…”

A Cayley–Bacharach theorem for points in Pn

“…More generally, if C 1 , C 2 ⊆ P 2 are two curves of degrees d 1 d 2 meeting transversely in d 1 d 2 points, the Cayley-Bacharach theorem states that, if a curve X of degree D = d 1 + d 2 − 3 passes through all but possibly one point of C 1 ∩ C 2 , then it must contain all d 1 d 2 points of C 1 ∩ C 2 . In the literature, there have been several efforts to extend this theorem to a more general setup [11,19,22,25,26,30]. However, in most cases, the obtained results still require the hypersurface to pass through at least all but one point.…”

“…In the literature, there have been several efforts to extend this theorem to a more general setup [11,19,22,25,26,30]. However, in most cases, the obtained results still require the hypersurface to pass through at least all but one point.…”