Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

30^th of March 2024, 14:30-16:00, room “D’Antoni”

 

 

 

 

 

 

Hyperelliptic curves and differentials

 

Luca Battistella

Università di Bologna

 

 

 

Strata of differentials have been studied from several
perspectives, from dynamics to geometry and topology. Algebraic geometers
need compactifications. One, which is a posteriori logarithmic, was
introduced by Bainbridge--Chen--Gendron--Grushevsky--Möller in terms of
multiscale (collections of) differentials (on reducible nodal curves). This
natural compactification is unfortunately not irreducible, but they were
able to single out the main component in terms of a condition on global
residues; their proof rests on transcendental methods. I will mention a
conjecturally equivalent condition which is purely algebraic. In joint work
with Sebastian Bozlee, we give a proof of concept of this conjecture in the
case of hyperelliptic differentials. The technical core of our work is a
flexible tool for constructing hyperelliptic Gorenstein contractions of
reducible nodal curves, given a hyperelliptic tropical differential, i.e. a
suitable piecewise-linear function, on the dual graph.

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry