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SUMMARY:Hannah Larson (Stanford University)
DTSTART:20200903T181000Z
DTEND:20200903T191000Z
DTSTAMP:20260423T004915Z
UID:MAGIC/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAGIC/16/">B
 rill--Noether theory over the Hurwitz space</a>\nby Hannah Larson (Stanfor
 d University) as part of MAGIC (Michigan - Arithmetic Geometry Initiative 
 - Columbia)\n\n\nAbstract\nLet $C$ be a curve of genus $g$. A fundamental 
 problem in the theory of algebraic curves is to understand maps of $C$ to 
 projective space of dimension r of degree d. When the curve $C$ is general
 \, the moduli space of such maps is well-understood by the main theorems o
 f Brill-Noether theory.  However\, in nature\, curves $C$ are often encoun
 tered already equipped with a map to some projective space\, which may for
 ce them to be special in moduli.  The simplest case is when $C$ is general
  among curves of fixed gonality.  Despite much study over the past three d
 ecades\, a similarly complete picture has proved elusive in this case. In 
 this talk\, I will discuss recent joint work with Eric Larson and Isabel V
 ogt that completes such a picture\, by proving analogs of all of the main 
 theorems of Brill--Noether theory in this setting.\n\nThere is a pre-talk 
 by Eric Larson on limit linear series.\n
LOCATION:https://researchseminars.org/talk/MAGIC/16/
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