Classical Brill–Noether theory concerns the following question: if C is a general algebraic curve of genus g, and we fix two positive integers a and b, what is the geometry of the locus of line bundles L on C such that h⁰(L) = a and h¹(L) = b? I will describe a refinement of this question for twice-marked curves (C,p,q), in which one specifies vanishing and pole orders at the marked points. I will refer to these as transmission loci. Transmission loci provide a convenient tool in degeneration arguments, and their geometry contains rich combinatorics arising from the theory of integer permutations. I will discuss some analogs of classical Brill–Noether theory for transmission loci, and some open problems.
Brill–Noether theory of twice-marked curves via integer permutations
Időpont:
2026. 03. 10. 10:30
Hely:
H306
Előadó:
Nathan Pflueger (Amherst College)

