IJPAM: Volume 61, No. 4 (2010)

ON THE POSTULATION OF A GENERAL UNION OF
TRIPLE POINTS AND DOUBLE POINTS IN $\mathbb {P}^4$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Fix integers $d, x, y$ such that $d \ge 8$, $x \ge 0$, $y \ge 0$. Let $Z \subset \mathbb {P}^4$ be a general union of $x$ triple points and $y$ double points. Here we prove that either $h^1(\mathbb {P}^4,\mathcal {I}_Z(d)) = 0$ (case $15x+5y \le \binom{d+4}{4}$) or $h^0(\mathbb {P}^4,\mathcal {I}_Z(d)) = 0$ (case $15x+5y \ge \binom{d+4}{4}$). When $d=7$ we are only able to prove the corresponding result assuming $(x,y) \notin \{ (22,0),(21,3)\}$.

Received: April 17, 2010

AMS Subject Classification: 14N05, 15A72, 65D05

Key Words and Phrases: polynomial interpolation, zero-dimensional scheme, fat point, triple point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 4