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DTSTART;TZID=America/Toronto:20250311T130000
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URL:https://uwaterloo.ca/pure-mathematics/events/algebraic-geometry-working
 -seminar-87
SUMMARY:Algebraic Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:ROBERT CORNEA\, UNIVERSITY OF WATERLOO\n\nStable Pairs on P2 vi
 a Spectral Correspondence\n\nIn this talk we will consider stable wild Vaf
 a-Witten-Higgs bundles\n(or stable pairs for short) (E\, ϕ) on P^2 where 
 E is a rank two\nholomorphic vector bundle and ϕ : E -> E(d) is a holomor
 phic bundle\nmap with d > 0. There is a way to construct stable pairs on c
 alled the\nspectral correspondence. This states that given a stable pair (
 E\,ϕ)\non P^2\, there exists a surface Y and a 2:1 covering map pi: Y -> 
 P^2\nsuch that E is the push forward of a line bundle on Y and ϕ comes\nf
 rom the multiplication of a section on Y. So studying stable pairs\n(E\,ϕ
 ) on P^2 boils down to finding 2:1 covering maps Y -> P^2 and\nline bundle
 s on Y. The study of constructing rank two vector bundles\non P^2 via 2:1 
 coverings was studied by Schwarzenberger in 1960. We\nwill demonstrate exa
 mples of stable pairs when d=1 and explain the\ncases briefly for d=2 and 
 3.\n\nMC 5479
DTSTAMP:20260504T161333Z
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