By interpreting 1 as the unique complex quadratic form z->z^2, some classical
enumerations (i.e. with values in $\mathbb N$) acquire meaning when the field of
complex numbers is replaced with an arbitrary field $k$. The result of the enumeration
is then a quadratic form over $k$ rather than an integer.
This talk will focus on such enumeration for rational curves in del Pezzo surfaces. In
particular I will report on a recent joint work with Kirsten Wickelgren where we
generalize a formula originally due to Abramovich and Bertram in the complex setting,
that I later extended over the real numbers. This quadratically enriched version of
the AB-formula relates enumerative invariants for different $k$-forms on the same del
Pezzo surfaces.
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