arXiv:1711.04906v2 [math.AG] 18 Sep 2018 The Maximal Rank Conjecture Page 1 arXiv:1711.04906v2
[math.AG] 18 Sep 2018 The Maximal Rank Conjecture Eric Larson Abstract Let C be a general …

Interpolation for Brill–Noether curves Page 1 Forum of Mathematics, Pi (2023), Vol. 11:e25 1–90
doi:10.1017/fmp.2023.22 RESEARCH ARTICLE Interpolation for Brill–Noether curves Eric …

A fundamental problem in the theory of algebraic curves in projective space is to understand
which reducible curves arise as limits of smooth curves of general moduli. Special cases of …

We prove that the normal bundle of a general Brill–Noether space curve of degree d and
genus g≥ 2 is stable if and only if (d, g)∉{(5, 2),(6, 4)}. When g≤ 1 and the characteristic of …

arXiv:1809.05980v1 [math.AG] 16 Sep 2018 Degenerations of Curves in Projective Space
and the Maximal Rank Conjecture Page 1 arXiv:1809.05980v1 [math.AG] 16 Sep 2018 …

We compute the number of general points through which a general Brill–Noether curve in P^
4 P 4 passes. We also prove an analogous theorem when some points are constrained to lie …

This paper is the second of a two-part series by the author devoted to the following
fundamental problem in the theory of algebraic curves in projective space: Which reducible …

We prove that the normal bundle of a general Brill–Noether curve of genus g≥ 1 and
degree d in P r is semistable if g= 1 or or d is larger than an explicit function of g and r. We …

A classical fact is that through any $ d+ 3$ general points in $\mathbb {P} _\mathbb {C}^ d $
there exists a unique rational normal curve of degree $ d $ passing through them. We …

Given general points it is natural to ask whether there is a curve of given degree and genus
passing through them; by counting dimensions a natural conjecture is that such a curve …