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SUMMARY:Hannah Larson (Harvard/Berkeley)
DTSTART:20230505T190000Z
DTEND:20230505T200000Z
DTSTAMP:20260407T214747Z
UID:agstanford/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 10/">The embedding theorem in Hurwitz--Brill--Noether theory</a>\nby Hanna
 h Larson (Harvard/Berkeley) as part of Stanford algebraic geometry seminar
 \n\nLecture held in Room 383-N.\n\nAbstract\nBrill--Noether theory studies
  the maps of general curves to projective spaces. The embedding theorem of
  Eisenbud and Harris states that a general degree $d$ map $C \\rightarrow 
 \\mathbb{P}^r$ is an embedding when $r \\geq 3$. Hurwitz--Brill--Noether t
 heory starts with a curve $C$ already equipped with a fixed map $C \\right
 arrow \\mathbb{P}^1$ (which often forces $C$ to be special) and studies th
 e maps of $C$ to other projective spaces. In this setting\, the appropriat
 e analogue of the invariants $d$ and $r$ is a finer invariant called the s
 plitting type. Our embedding theorem determines the splitting types $\\vec
 {e}$ such that a general map of splitting type $\\vec{e}$ is an embedding.
  This is joint work with Kaelin Cook--Powel\, Dave Jensen\, Eric Larson\, 
 and Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/agstanford/110/
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