arXiv subjects

Sean Keel

Publications and source records attributed to Sean Keel.

22 records · Page 2Linked to original sources

arXiv1998

Basepoint freeness for big line bundles in positive characteristic, with applications to M_g and to 3-fold MMP

I give a necessary and sufficient condition for a nef and big line bundle in positive characteristic to be semi-ample, and then give two applications: I show that the relative dualizing sheaf of the universal curve is semi-ample, in positive characteristic, and give a simple example which shows that this, and the semi-ampleness criterion, fail in characteristic zero. My second application is to Mori's program for minimal models of 3-folds. I prove a version of the Basepoint Free Theorem (for big line bundles on 3-folds of positive characteristic) and a simple Cone Theorem, for 3-folds of positive Kodaira dimension.

alg-geom↗

arXiv1997

Rational Curves on Quasi-Projective Surfaces

The main result is that a quasi-projective surface has negative log Kodaira dimension (i.e. no log pluricanonical sections) iff it is dominated by images of the affine line. This follows from our main intermediate result, that the smooth locus of a log Fano surface is rationally connected. We also give a classification of all but a bounded family of rank one log del Pezzo surfaces.

alg-geom↗

arXiv1996

Contractible Extremal Rays on \overline{M}_{0,n}

We consider the cones of curves and divisors on the moduli space of stable pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n, which is a moduli space of pairs. We find generators for contractible extremal rays of the cone of curves NE_1(M_n), and for the cone of divisors NE^1(Q_n). This second cone turns out to be simplicial. We give complete descriptions of NE_1(M_n) and NE_1(Q_n) for small n (< 8 in the first case, < 11 in the second). We also have results of independent interest on when curves in a divisor generate the cone of curves of the ambient variety.

alg-geom↗

arXiv1995

Quotients by Groupoids

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite has a uniform geometric, uniform categorical quotient in the category of algebraic spaces. Our argument is elementary and essentially self contained.

alg-geom↗