Seminar in Real & Complex Geometry
Wednesday, 09.10.2013, 11:00-12:30,
Schreiber
building, room 209
Franziska Schroeter,
Universitaet des Saarlandes
Refined Broccoli invariants
Abstract
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 Go"ttsche recently introduced
polynomial multiplicities (in the variable y) for plane tropical curves
which yield an invariant number when we count 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.
In this talk I present a similar approach for broccoli invariants which
have been introduced to prove the invariance of tropical Welschinger
numbers for certain real curves. Endowing each broccoli curve with a
polynomial multiplicity yields again an invariant and this approach can be
used to find simpler Caporaso Harris type formulas for broccoli
invariants.
This is joint work in progress with Lothar Goettsche.
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