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Concurrent lines on del Pezzo surfaces of degree one

Concurrent lines on del Pezzo surfaces of degree one

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a del Pezzo surface of degree one over an algebraically closed field, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K Subscript upper X"> <mml:semantics> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">K_X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> its canonical divisor. …