Geometry of families of nodal curves on the blown-up projective plane
Geometry of families of nodal curves on the blown-up projective plane
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper P Subscript r Superscript 2"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:mrow> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mspace width="thinmathspace"/> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb P^2_r\,</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the projective plane blown up at <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="r"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding="application/x-tex">r</mml:annotation> </mml:semantics> </mml:math> …