plotting – “Poor” export quality for SVG image

I export an image in SVG format using the Export command (code below). I find the quality okayish, but not great. I tried playing around with PlotPoints and MaxRecursion, but without being able to improve things significantly. Are there other parameters for ParametricPlot and/or Export that can improve the output quality?

xmin = -1;
xmax = 1;
ymin = -1.5;
ymax = 1.5;
darkblue = RGBColor("#004699");
lightblue = RGBColor("#0071b9");
thick = 0.001;

f(x_, y_) := {Exp(x)*Cos(y), Exp(x)*Sin(y)};

F(x_, y_, t_) := (1 - t)*{x, y} + t*f(x, y);

t = 0.75;

homotopy = Table(ParametricPlot({F(i, j + s*ymax, t), F(i + s*xmax, j, t)}, {s, -5, 5}, PlotStyle -> {{If(i == 0, darkblue, If(i == Floor(i), lightblue, Black)), If(i == 0, Thickness(5*thick), If(i == Floor(i), Thickness(3*thick),Thickness(thick/10)))}, {If(j == 0, darkblue,If(j == Floor(j), lightblue, Black)), If(j == 0,Thickness(5*thick),If(j == Floor(j), Thickness(3*thick), Thickness(thick/10)))}},PlotRange -> {{xmin, xmax}, {ymin, ymax}}, PlotPoints -> 100,MaxRecursion -> 15, Background -> None, PlotRangeClipping -> True,Axes -> False), {i, 2*xmin, 2*xmax, 1}, {j, 5*ymin, 5*ymax, 1});

Export("~/Desktop/homotopy.svg",Show(homotopy));