[Dottorcomp] Seminari di Algebra e Geometria - mercoledì 10 aprile 2024

[Lidia Stoppino]

Il giorno mercoledì 10 aprile 2024
alle 16,30 in aula Beltrami 

Il Professor Michele Bolognesi (Université de Montpellier)
terrà un seminario dal titolo:

Odd determinant moduli spaces of vector bundles on a genus 2 curve

Abstract: 
Let C be a smooth genus two curve. The moduli space SU_C(3) of rank three semistable vector bundles on C with trivial determinant a double cover of P8 branched over a sextic hypersurface, whose projective dual is the famous Coble cubic, the unique cubic hypersurface that is singular along the Jacobian of C. Let V be a 9-dimensional complex vector space. Starting from a general trivector v in wedge^3(V), I will construct a Fano manifold D_{Z_10}(v) inside the Grassmannian G(3,9) as an orbital degeneracy locus. It turns out that D_{Z_10} naturally defines a family of Hecke lines in SU_C(3). With some work, this property allows us to deduce that D_{Z_10}(v) is isomorphic to the odd moduli space SU_C(3,O_C(c)) of rank three stable vector bundles on C with fixed effective determinant of degree one. As a side result, I will show that the intersection of D_{Z_10}(v) with a general translate of G(3,7) inside G(3,9) is a K3 surface of genus 19, for which a "Mukai model" did not exist. This is joint work with V. Benedetti, D. Faenzi and L. Manivel


Tutti gli interessati sono cordialmente invitati a partecipare. 

Chi vuole venire a cena scriva tempestivamente a me, a filippo Favale <filippo.favale a unipv.it> e a Davide Bricalli <davide.bricalli a unipv.it>.


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Lidia Stoppino
Dipartimento di Matematica
Università di Pavia
Via Ferrata 5
27100 Pavia
Ufficio C.07 (primo piano)
Tel. +39 0382 985624
e-mail: lidia.stoppino a unipv.it 
pagina web: http://www.stoppino.it