We briefly survey recent results related to linear series on curves that are general in various
moduli spaces, highlighting the interplay between algebraic geometry on a general curve …

Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a
distinguished map to the projective line. We give a tropical proof of a theorem of H. Larson …

Higher rank Brill—Noether theory and coherent systems open questions Page 1 Higher rank
Brill—Noether theory and coherent systems open questions Peter E. Newstead University of …

We prove an analogue of Kirchhoff's matrix tree theorem for computing the volume of the
tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of …

We propose a definition of tropical linear series that isolates some of the essential
combinatorial properties of tropicalizations of not-necessarily-complete linear series on …

In this paper, we describe the Brill--Noether theory of a general smooth plane curve and a
general curve $ C $ on a Hirzebruch surface of fixed class. It is natural to study the line …

We provide a new geometric interpretation of the multidegrees of the (iterated) Kapranov
embedding $\Phi_n:\overline {M} _ {0, n+ 3}\hookrightarrow\mathbb {P}^ 1\times\mathbb …

The moduli space G g, dr→ M g parameterizing algebraic curves with a linear series of
degree 𝑑 and rank 𝑟 has expected relative dimension ρ= g−(r+ 1)⁢(g− d+ r). Classical Brill …

The interpolation problem is a natural and fundamental question whose roots trace back to
ancient Greece. The story is long and rich, with many chapters, and a complete solution has …

Coxeter groups possess an associative operation, called variously the Demazure, greedy, or
$0 $-Hecke product. For symmetric groups, this product has an amusing formulation as …