= Relative effective Cartier divisor on a curve
{title2=$D\subset C\times T$}
= Relative effective Cartier divisors on a curve
{synonym}
A relative effective divisor of degree $m$ on a <smooth projective curve> is an <effective Cartier divisor> in $C\times T$ that is finite and flat of degree $m$ over $T$. Its associated <line bundle> has degree $m$ on every fibre. The <symmetric product of a curve> $C^{(m)}$ represents these families and carries their universal divisor. Locally on a smooth coordinate chart, the divisor is described by a monic polynomial, whose coefficients are elementary symmetric functions of its points; this description includes collisions and works in positive characteristic.
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