Global aspects of the geometry of surfaces

By Brian Harbourne. 2009

62 citations recorded by the source corpus.

These notes (prepared for the author's lectures at the Cracow Summer School on Linear Systems organized by S. Mueller-Stach and T. Szemberg, held March 23-27, 2009 at the Pedagogical University of Cracow under the sponsorship of the Deutsche Forschungsgemeinschaft) present a number of open problems on the theory of smooth projective algebraic surfaces, and put into historical context recent work on a range of topics, including Mori dream spaces and the finite generation of the Cox ring, Seshadri constants, and the resurgence of homogeneous ideals and the problem of which ordinary powers of homogeneous ideals contain given symbolic powers of those ideals. These notes include many exercises, with solutions.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72c633206727dd3b5abe3e42c78bd140e03e32cf

How researchers see this paper

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In Algebra and Number Theory

1. Tomasz Szemberg
2. Brian Harbourne
3. Thomas Bauer
4. Sandra Di Rocco
5. Cristiano Bocci

In Geometry and Topology

1. Tomasz Szemberg
2. Brian Harbourne
3. Thomas Bauer
4. Jack Huizenga
5. Sandra Di Rocco
6. Cristiano Bocci

Citations in the corpus

• Bounded Negativity and Arrangements of Lines (2014, background): “nts. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10. 1 Introduction In recent years there has been growing interest in constraints on negative curves on algebraic surfaces [2, 3, 5, 6, 11, 15, 17]. The Bounded Negativity Conjecture (BNC for short) is probably the most int”