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Singularities and Computer Algebra pp 275–304Cite as

On Welschinger Invariants of Descendant Type

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Abstract

We introduce enumerative invariants of real del Pezzo surfaces that count real rational curves belonging to a given divisor class, passing through a generic conjugation-invariant configuration of points and satisfying preassigned tangency conditions to given smooth arcs centered at the fixed points. The counted curves are equipped with Welschinger-type signs. We prove that such a count does not depend neither on the choice of the point-arc configuration nor on the variation of the ambient real surface. These invariants can be regarded as a real counterpart of (complex) descendant invariants.

Dedicated to Gert-Martin Greuel in occasion of his 70th birthday

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Acknowledgements

The author has been supported by the grant no. 1174-197.6/2011 from the German-Israeli Foundations, by the grant no. 176/15 from the Israeli Science Foundation and by a grant from the Hermann Minkowski–Minerva Center for Geometry at the Tel Aviv University.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Eugenii Shustin

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  1. Eugenii Shustin
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Correspondence to Eugenii Shustin .

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Editors and Affiliations

  1. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

    Wolfram Decker

  2. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

    Gerhard Pfister

  3. Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany

    Mathias Schulze

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Shustin, E. (2017). On Welschinger Invariants of Descendant Type. In: Decker, W., Pfister, G., Schulze, M. (eds) Singularities and Computer Algebra. Springer, Cham. https://doi.org/10.1007/978-3-319-28829-1_13

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