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

[Valentina Beorchia]

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  
varieties

Abstract:
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.

Join Zoom Meeting
https://us02web.zoom.us/j/86450056367?pwd=VjR0UGI0dDMyU29uaDBkSGVYL3V2dz09

Meeting ID: 864 5005 6367
Password: 568955
One tap mobile
+13017158592,,86450056367#,,1#,568955# US (Germantown)
+13126266799,,86450056367#,,1#,568955# US (Chicago)

Dial by your location
         +1 301 715 8592 US (Germantown)
         +1 312 626 6799 US (Chicago)
         +1 346 248 7799 US (Houston)
         +1 669 900 6833 US (San Jose)
         +1 929 205 6099 US (New York)
         +1 253 215 8782 US (Tacoma)
Meeting ID: 864 5005 6367
Password: 568955
Find your local number: https://us02web.zoom.us/u/kef1LY9aZU

-------------------------------------------
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 units.it
Tel.| Ph. +39 040 5582656
Skype: valbeo