Algebraic Geometry Seminar (Zoom Meeting): 3rd June, 16:30 (Elisabetta Colombo)

Valentina Beorchia beorchia at
Thu May 28 23:24:57 CEST 2020

Algebraic Geometry Seminar (Zoom Meeting)

When: Wednesday 3rd June, at 16:30

Speaker: Elisabetta Colombo (Università di Milano)

Title: On the dimension of Voisin sets in the moduli space of abelian  

I will discuss research done in collaboration with J.C. Naranjo and  
G.P. Pirola on the subsets Vk(A) of a complex abelian variety A  
consisting of the points x ∈ A such that the zero-cycle {x}−{0A} is  
k-nilpotent with respect to the Pontryagin product in CH0(A). These  
sets were introduced by Voisin in Chow rings and gonality of general  
abelian varieties, Ann. H. Lebesgue, I (2018). She showed that dim Vk  
(A) ≤ k − 1 and this dimension is zero for a general abelian variety  
of dimension at least 2k − 1.
We study in particular the locus Vg,2 in the moduli space of abelian  
varieties of dimension g with a fixed polarization of the A for which  
V2(A) is positive dimensional and we prove
Theorem Let g ≥ 3 and consider an irreducible subvariety Y ⊂ Vg,2 such  
that for a very general A ∈ Y there is a curve in V2(A) generating A.  
Then dim Y ≤2g−1.
The hyperelliptic locus shows that this bound is sharp.

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Valentina Beorchia

Ricercatrice Universitaria | Assistant Professor
Università degli Studi di Trieste | University of Trieste
Dipartimento di Matematica e Geoscienze
Sezione di Matematica e Informatica
Via Valerio, n 12/1 - 34127 Trieste (Italy)
beorchia at
Tel.| Ph. +39 040 5582656
Skype: valbeo

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