Seminari del Dipartimento

 

Geometria

Deformations of hypersurfaces with non-constant Alexander polynomial

Remke Kloosterman


26-05-2022 - 14:15
Largo San Leonardo Murialdo, 1

 

Let X be an irreducible hypersurface in P^n of degree d. If X has isolated singularities then h^i(X)=h^i(P^n) holds for i∉{????n−1,n,2n−2}????. Most hypersurfaces with isolated singularities satisfy h^n(X)=h^n(Pn). In this talk we consider hypersurfaces with semi-weighted homogeneous (e.g., ordinary multiple points or ADE-singularities) such that h^n(X)>h^n(P^n) holds. We show that if (d,n) is not in an explicit finite list then the equianalytic deformation space of X is not T-smooth, i.e., this space is nonreduced or its dimension is larger than expected. A similar statement holds true for X if the d-fold cover Y of Pn ramified along X satisfies h^{??n+1}??(Y)>h^{??n+1}??(P^{??n+1}??). This latter result generalizes classical examples of B. Segre of degree 6m curves in P^2 with 6m^2, 7m^2, 8m^2 and 9m^2 cusps and deformation space larger than expected.

Il seminario sarà presentato in presenza nell'aula M3. Gli esterni che fossero interessati a partecipare possono contattare gli organizzatori all'email amos.turchet@uniroma3.it.

Il seminario sarà anche seguibile via Teams seguendo il seguente link:

https://teams.microsoft.com/l/meetup-join/19%3a83395ad07b844acdafb3fff3e977ef5d%40thread.tacv2/1653039838396?context=%7b%22Tid%22%3a%22ffb4df68-f464-458c-a546-00fb3af66f6a%22%2c%22Oid%22%3a%22cade3502-1fa9-4fd8-a9e6-8a2cc994de29%22%7d
org: Turchet Amos

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