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SUMMARY:The logarithmic Hilbert scheme and it’s tropicalisation - Patric
 k Kennedy-Hunt (University of Cambridge)
DTSTART:20230607T131500Z
DTEND:20230607T141500Z
UID:TALK201073@talks.cam.ac.uk
CONTACT:Holly Krieger
DESCRIPTION:The Hilbert scheme of a projective variety X is the moduli spa
 ce of closed subschemes of X. In this talk we discuss a version of the Hil
 bert scheme for a pair (X\,D) with D a (reasonable) divisor on X. This log
 arithmic Hilbert scheme is the most intuitive example of the logarithmic Q
 uot scheme. There is a closely related tropical moduli problem called the 
 stack of tropical supports. This tropical problem is reminiscent of a trop
 ical version of a Hilbert scheme.  As motivation\, note hard algebraic geo
 metry problems can be studied by degenerating to simpler situations. Logar
 ithmic geometry provides a suite of tools to study such degenerations. A l
 ong term hope is to study other moduli spaces of coherent sheaves with log
 arithmic geometry.
LOCATION:CMS MR13
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