On Welschinger Invariants of Descendant Type

  • Eugenii ShustinEmail author


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.


del Pezzo surfaces Descendant invariants Real enumerative geometry Real rational curves Welschinger invariants 

Subject Classification:

Primary 14N35; Secondary 14H10 14J26 14P05 



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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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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