# Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicity

@article{Yang2004LinearSI, title={Linear systems in \$\mathbb\{P\}^2\$ with base points of bounded multiplicity}, author={Stephanie Yang}, journal={Journal of Algebraic Geometry}, year={2004}, volume={16}, pages={19-38} }

We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that arises from specializing points onto a line.

## 14 Citations

### New results on fat points schemes in $\mathbb{P}^2$

- Mathematics
- 2013

The purpose of this note is to announce two results, Theorem A and Theorem B below, concerning geometric and algebraic properties of fat points in the complex projective plane. Their somewhat…

### Cutting diagram method for systems of plane curves with base points

- Mathematics
- 2007

We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz– Harbourne conjecture holds for systems…

### On the minimal free resolution for fat point schemes of multiplicity at most 3 in P^2

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- 2007

### INTERPOLATION ON SURFACES IN P

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- 2012

Suppose S is a surface in P3, and p1, . . . , pr are general points on S. What is the dimension of the space of sections of OS(e) having singularities of multiplicity mi at pi for all i? We formulate…

### Betti numbers for fat point ideals in the plane: a geometric approach

- Mathematics
- 2007

We consider the open problem of determining the graded Betti numbers for fat point subschemes Z supported at general points of P 2 . We relate this problem to the open geometric problem of…

### Towards Mori’s program for the moduli space of stable maps

- Mathematics
- 2009

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps $\overline{{\scr M}}_{0,0}({\Bbb P}^{r}, d)$, which, for small $d$, provide a good…

### Harbourne–Hirschowitz surfaces whose anticanonical divisors consist only of three irreducible components

- MathematicsInternational Journal of Mathematics
- 2018

In this paper, we provide new families of Harbourne–Hirschowitz surfaces whose effective monoids are finitely generated, and consequently, their Cox rings are finitely generated. Indeed, these…

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