Plane curves with ordinary multiple points and variables ordinary nodes

E. Ballico
2007 International Journal of Contemporary Mathematical Sciences  
Fix integers s > 0, m i > 0, 1 ≤ i ≤ s, d > 0, z ≥ 0, and s distinct points of P 2 . Let W (d; m 1 P 1 , . . . , m s P s ; z) denote the set of all integral degree d plane curves with an ordinary point with multiplicity m i at each P i and z ordinary nodes in P 2 \{P 1 , . . . , P s } as its only singularities. Here we show under certain assumptions (mainly if either s ≤ 5 or z 0) that W (d; m 1 P 1 , . . . , m s P s ; z) and with the expected dimension. Mathematics Subject Classification: 14H50
doi:10.12988/ijcms.2007.07017 fatcat:picf5qdx3jbrzm5kdcq2bskzl4