TY - JOUR
T1 - Relative enumerative invariants of real nodal del Pezzo surfaces
AU - Itenberg, Ilia
AU - Kharlamov, Viatcheslav
AU - Shustin, Eugenii
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - The surfaces considered are real, rational and have a unique smooth real (- 2) -curve. Their canonical class K is strictly negative on any other irreducible curve in the surface and K2> 0. For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the (- 2) -curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the (- 2) -curve.
AB - The surfaces considered are real, rational and have a unique smooth real (- 2) -curve. Their canonical class K is strictly negative on any other irreducible curve in the surface and K2> 0. For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the (- 2) -curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the (- 2) -curve.
UR - http://www.scopus.com/inward/record.url?scp=85048106538&partnerID=8YFLogxK
U2 - 10.1007/s00029-018-0418-y
DO - 10.1007/s00029-018-0418-y
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AN - SCOPUS:85048106538
SN - 1022-1824
VL - 24
SP - 2927
EP - 2990
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 4
ER -