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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Complex dynamics: degenerations\, and irreducibili
ty problems - Rohini Ramadas\, University of Warwi
ck
DTSTART;TZID=Europe/London:20221012T141500
DTEND;TZID=Europe/London:20221012T151500
UID:TALK178931AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178931
DESCRIPTION:Per_n is an affine algebraic curve\, defined over
Q\, parametrizing (up to change of coordinates) de
gree-2 self-morphisms of P^1 with an n-periodic ra
mification point. The n-th Gleason polynomial G_n
is a polynomial in one variable with Z-coefficient
s\, whose vanishing locus parametrizes (up to chan
ge of coordinates) degree-2 self-morphisms of C wi
th an n-periodic ramification point. Two long-stan
ding open questions in complex dynamics are: (1) I
s Per_n is irreducible over C? (2) Is G_n is irred
ucible over Q? \n\nWe show that if G_n is irreduci
ble over Q\, then Per_n is irreducible over C. In
order to do this\, we find a Q-rational smooth poi
nt of a projective completion of Per_n. This Q-rat
ional smooth point represents a special degenerati
on of degree-2 morphisms\, and as such admits a tr
opical interpretation.
LOCATION:CMS MR13
CONTACT:Dhruv Ranganathan
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