On the Geometry of the Hilbert Schemes of Points in the Projective Plane
نویسندگان
چکیده
We determine the nef cone and effective cone of the Hilbert scheme X[n] of points on the projective plane X = P2, characterize all the rational curves in X[n] of degree-1 with respect to some very ample line bundle, describe the moduli spaces of these curves, and study the contraction of the extremal ray on X[n]. Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong Department of Mathematics, University of Missouri, Columbia, MO 65211, USA
منابع مشابه
The Cohomology Rings of Hilbert Schemes via Jack Polynomials
Fundamental and deep connections have been developed in recent years between the geometry of Hilbert schemes X [n] of points on a (quasi-)projective surface X and combinatorics of symmetric functions. Among distinguished classes of symmetric functions, let us mention the monomial symmetric functions, Schur polynomials, Jack polynomials (which depend on a Jack parameter), and Macdonald polynomia...
متن کاملSklyanin Algebras and Hilbert Schemes of Points
We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective plane P. The generic noncommutative plane corresponds to the Sklyanin algebra S = Skl(E,σ) constr...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملThe geometry of the parabolic Hilbert schemes
Let X be a smooth projective surface and D be a smooth divisor over an algebraically closed field k. In this paper, we discuss the moduli schemes of the ideals of points of X with parabolic structures at D. They are called parabolic Hilbert schemes. The first result is that the parabolic Hilbert schemes are smooth. And then some of the studies of Ellingsrud-Strømme, Göttsche, Cheah, Nakajima an...
متن کامل1-point Gromov-witten Invariants of the Moduli Spaces of Sheaves over the Projective Plane
The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points. When the surface is the complex projective plane, we determine all the 1-point genus-0 Gromov-Witten invariants extremal with respect to the Gieseker-Uhlenbeck...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008