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SUMMARY:Hannah Larson (Stanford University)
DTSTART;VALUE=DATE-TIME:20200821T190000Z
DTEND;VALUE=DATE-TIME:20200821T200000Z
DTSTAMP;VALUE=DATE-TIME:20211209T074313Z
UID:agstanford/19
DESCRIPTION:Title: Brill--Noether theory over the Hurwitz space\nby Hannah Larson (St
anford University) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nLet $C$ be a curve of genus $g$. A fundamental problem in the theor
y 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 of Brill-Noether theo
ry. However\, in nature\, curves $C$ are often encountered already equipp
ed with a map to some projective space\, which may force them to be specia
l in moduli. The simplest case is when $C$ is general among curves of fix
ed gonality. Despite much study over the past three decades\, a similarly
complete picture has proved elusive in this case. In this talk\, I will d
iscuss recent joint work with Eric Larson and Isabel Vogt that completes s
uch a picture\, by proving analogs of all of the main theorems of Brill--N
oether theory in this setting.\n\nThe discussion for Hannah Larsonâ€™s tal
k is taking place not in zoom-chat\, but at https://tinyurl.com/2020-08-21
-hl (and will be deleted after 3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/19/
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