2,998 research outputs found
Nakamaye's theorem on log canonical pairs
We generalize Nakamaye's description, via intersection theory, of the
augmented base locus of a big and nef divisor on a normal pair with
log-canonical singularities or, more generally, on a normal variety with non-lc
locus of dimension at most 1. We also generalize
Ein-Lazarsfeld-Mustata-Nakamaye-Popa's description, in terms of valuations, of
the subvarieties of the restricted base locus of a big divisor on a normal pair
with klt singularities.Comment: v2: We removed, in the introduction, the phrase about Choi's papers,
as he uses Nakamaye's theorem in the semiample case. Updated references. v3:
added reference to Ambro's "Quasi-log varieties". v4: improved exposition in
sections 1, 2 and 4; slightly corrected the statement of Lemma 3.
Enumeration of surfaces containing an elliptic quartic curve
A very general surface of degree at least four in projective space of
dimension three contains no curves other than intersections with surfaces. We
find a formula for the degree of the locus of surfaces of degree at least five
which contain some elliptic quartic curve. We also compute the degree of the
locus of quartic surfaces containing an elliptic quartic curve, a case not
covered by that formula.Comment: Minor typos corrected. To appear on Proceedings of the American
Mathematical Societ
Efficiency of a stirred chemical reaction in a closed vessel
We perform a numerical study of the reaction efficiency in a closed vessel.
Starting with a little spot of product, we compute the time needed to complete
the reaction in the container following an advection-reaction-diffusion
process. Inside the vessel it is present a cellular velocity field that
transports the reactants. If the size of the container is not very large
compared with the typical length of the velocity field one has a plateau of the
reaction time as a function of the strength of the velocity field, . This
plateau appears both in the stationary and in the time-dependent flow. A
comparison of the results for the finite system with the infinite case (for
which the front speed, , gives a simple estimate of the reacting time)
shows the dramatic effect of the finite size.Comment: 4 pages, 4 figure
Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds
In this article we exhibit certain projective degenerations of smooth
surfaces of degree in (whose Picard group is generated by the
hyperplane class), to a union of two rational normal scrolls, and also to a
union of planes. As a consequence we prove that the general hyperplane section
of such surfaces has a corank one Gaussian map, if or .
We also prove that the general such hyperplane section lies on a unique
surface, up to projectivities. Finally we present a new approach to the
classification of prime Fano threefolds of index one, which does not rely on
the existence of a line.Comment: 24 pages, AMS-LaTeX 1.
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