Block Göttsche Multiplicities and Broccoli Invariants

Seminar: 
Algebraic and Tropical Geometry
Event time: 
Thursday, September 4, 2014 - 11:00am to 12:00pm
Location: 
431 DL
Speaker: 
Franziska Schroeter
Speaker affiliation: 
University of Hamburg
Event description: 

Mikhalkin changed the way of considering enumerative problems in algebraic geometry when he considered tropical curves counted with a numerical multiplicity and proved that the invariance of classical enumerative numbers can be proven tropically. Block and Göttsche recently introduced polynomial multiplicities (in the variable $y$) for plane tropical curves which yield an invariant number when counting curves passing through a generic point configuration. In addition, they reveal deep relations to classical enumerative problems: specializing $y=1$ we obtain the corresponding Gromov Witten invariant and for $y=-1$ we retrieve the corresponding Welschinger invariant. After a recap of basic tropical notions, I will present a similar approach for broccoli invariants which have been introduced to prove the invariance of tropical Welschinger numbers for certain real curves.