Intersection of ACM-curves in P^3

Details Intersection of ACM-curves in P^3 Intersection of ACM-curves in P^3

2003-12-16

arxiv.org/abs/math/0312301v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen-Macaulay curves in $\PP^3$. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen-Macaulay curves $C_t$ and $C_{t-r}$ in $\PP^3$ defined by the maximal minors of a $t \times (t+1)$, resp. $(t-r) \times (t-r+1)$, matrix with linear entries, provided $C_{t-r}$ has no linear series of degree $d\leq{{t-r+1}\choose 3}$ and dimension $n\geq t-r$.

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