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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Complete Complexes and Spectral Sequences - Evange
los Routis\, University of Warwick
DTSTART;TZID=Europe/London:20191204T141500
DTEND;TZID=Europe/London:20191204T151500
UID:TALK132859AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/132859
DESCRIPTION:The space of complete collineations is an importan
t and beautiful chapter of algebraic geometry\, wh
ich has its origins in the classical works of Chas
les\, Schubert and many others\, dating back to th
e 19th century. It provides a 'wonderful compactif
ication' (i.e. smooth with normal crossings bounda
ry) of the space of full-rank maps between two (fi
xed) vector spaces. More recently\, the space of c
omplete collineations has been studied intensively
and has been used to derive groundbreaking result
s in diverse areas of mathematics. One such striki
ng example is L. Lafforgue's compactification of t
he stack of Drinfeld's shtukas\, which he subseque
ntly used to prove the Langlands correspondence fo
r the general linear group. \n\nIn joint work wit
h M. Kapranov\, we look at these classical spaces
from a modern perspective: a complete collineation
is simply a spectral sequence of two-term complex
es of vector spaces. We develop a theory involving
more full-fledged (simply graded) spectral sequen
ces with arbitrarily many terms. We prove that the
set of such spectral sequences has the structure
of a smooth projective variety\, the 'variety of c
omplete complexes'\, which provides a desingulariz
ation\, with normal crossings boundary\, of the 'B
uchsbaum-Eisenbud variety of complexes'\, i.e. a '
wonderful compactification' of the union of its ma
ximal strata.
LOCATION:CMS MR3
CONTACT:Dhruv Ranganathan
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