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Equivariant smoothings of cusp singularities

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dc.contributor.advisorPaul Hacking
dc.contributor.authorSIMONETTI, ANGELICA
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27T16:57:52.000
dc.date.accessioned2024-04-26T15:48:36Z
dc.date.available2024-04-26T15:48:36Z
dc.date.submittedSeptember
dc.date.submitted2021
dc.description.abstractLet $p \in X$ be the germ of a cusp singularity and let $\iota$ be an antisymplectic involution, that is an involution free on $X\setminus \{p\}$ and such that there exists a nowhere vanishing holomorphic 2-form $\Omega$ on $X\setminus \{p\}$ for which $\iota^*(\Omega)=-\Omega$. We prove that a sufficient condiition for such a singularity equipped with an antisymplectic involution to be equivariantly smoothable is the existence of a Looijenga (or anticanonical) pair $(Y,D)$ that admits an involution free on $Y\setminus D$ and that reverses the orientation of $D$.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/23342899
dc.identifier.orcidhttps://orcid.org/0000-0002-1609-6946
dc.identifier.urihttps://hdl.handle.net/20.500.14394/18675
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=3319&context=dissertations_2&unstamped=1
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/
dc.source.statuspublished
dc.subjectalgebraic geometry
dc.subjectLooijenga pairs
dc.subjectanticanonical pairs
dc.subjectcusp singularities
dc.subjectcusps
dc.subjectsmoothings
dc.subjectAlgebraic Geometry
dc.titleEquivariant smoothings of cusp singularities
dc.typeopenaccess
dc.typearticle
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:angelica.simonetti@gmail.com|institution:University of Massachusetts Amherst|SIMONETTI, ANGELICA
digcom.identifierdissertations_2/2355
digcom.identifier.contextkey23342899
digcom.identifier.submissionpathdissertations_2/2355
dspace.entity.typePublication
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