New examples of surgery invariant counts in real algebraic geometry

Abstract: Initial Welschinger invariants, as well as their various generalizations, are very sensitive, in general , to a change of topology of the underlying real structure. However, it was soon noticed that some natural combinations of them have a stronger invariance property (remaining also non-trivial in many interesting cases), the property that I call "surgery invariance": for a given complex deformation class of a variety, they no more depend on a chosen real structure. The starting example is the signed count of real lines on cubic surfaces in accordance with B.~Segre's division of such lines in 2 kinds, hyperbolic and elliptic. It is this example that originated a discovery of similar counts on higher dimensional hypersurfaces and complete intersections, and served as one of the impulses for a development of an integer valued real Schubert calculus. In this talk (based on a work in progress, joint with Sergey Finashin) I intend to discuss extending of the above cubic surface example in a bit different direction: from lines on a cubic surface to lines, and even higher degree rational curves, on other del Pezzo surfaces.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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