Welschinger invariants of toric Del Pezzo surfaces with nonstandard real structures |
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Authors: | E Shustin |
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Institution: | (1) School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel |
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Abstract: | The Welschinger invariants of real rational algebraic surfaces are natural analogs of the Gromov-Witten invariants, and they
estimate from below the number of real rational curves passing through prescribed configurations of points. We establish a
tropical formula for the Welschinger invariants of four toric Del Pezzo surfaces equipped with a nonstandard real structure.
Such a formula for real toric Del Pezzo surfaces with a standard real structure (i.e., naturally compatible with the toric
structure) was established by Mikhalkin and the author. As a consequence we prove that for any real ample divisor D on a surface Σ under consideration, through any generic configuration of c
1(Σ)D − 1 generic real points, there passes a real rational curve belonging to the linear system |D|.
To Vladimir Igorevich Arnold on the occasion of his 70th birthday |
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Keywords: | |
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