2,537 research outputs found
Quasi elementary contractions of Fano manifolds
Let X be a smooth complex Fano variety. We define and study 'quasi
elementary' contractions of fiber type f: X -> Y. These have the property that
rho(X) is at most rho(Y)+rho(F), where rho is the Picard number and F is a
general fiber of f. In particular any elementary extremal contraction of fiber
type is quasi elementary. We show that if Y has dimension at most 3 and Picard
number at least 4, then Y is smooth and Fano; if moreover rho(Y) is at least 6,
then X is a product. This yields sharp bounds on rho(X) when dim(X)=4 and X has
a quasi elementary contraction, and other applications in higher dimensions.Comment: Final version, minor changes, to appear in Compositio Mathematic
On some Fano manifolds admitting a rational fibration
Let X be a smooth, complex Fano variety. For every prime divisor D in X, we
set c(D):=dim ker(r:H^2(X,R)->H^2(D,R)), where r is the natural restriction
map, and we define an invariant of X as c_X:=max{c(D)|D is a prime divisor in
X}. In a previous paper we showed that c_X2, then either X
is a product, or X has a flat fibration in Del Pezzo surfaces. In this paper we
study the case c_X=2. We show that up to a birational modification given by a
sequence of flips, X has a conic bundle structure, or an equidimensional
fibration in Del Pezzo surfaces. We also show a weaker property of X when
c_X=1.Comment: 31 pages. Revised version, minor changes. To appear in the Journal of
the London Mathematical Societ
On Fano manifolds with a birational contraction sending a divisor to a curve
Let X be a smooth Fano variety of dimension at least 4. We show that if X has
an elementary birational contraction sending a divisor to a curve, then the
Picard number of X is smaller or equal to 5.Comment: 24 pages, 6 figure
Rank 2 quasiparabolic vector bundles on P1 and the variety of linear subspaces contained in two odd-dimensional quadrics
i
The number of vertices of a Fano polytope
Let X be a complex, Gorenstein, Q-factorial, toric Fano variety. We prove two
conjectures on the maximal Picard number of X in terms of its dimension and its
pseudo-index, and characterize the boundary cases. Equivalently, we determine
the maximal number of vertices of a simplicial reflexive polytope.Comment: Final version, to appear in Annales de l'Institut Fourie
Accurate fundamental parameters for Lower Main Sequence Stars
We derive an empirical effective temperature and bolometric luminosity
calibration for G and K dwarfs, by applying our own implementation of the
InfraRed Flux Method to multi-band photometry. Our study is based on 104 stars
for which we have excellent BVRIJHK photometry, excellent parallaxes and good
metallicities. Colours computed from the most recent synthetic libraries
(ATLAS9 and MARCS) are found to be in good agreement with the empirical colours
in the optical bands, but some discrepancies still remain in the infrared.
Synthetic and empirical bolometric corrections also show fair agreement. A
careful comparison to temperatures, luminosities and angular diameters obtained
with other methods in literature shows that systematic effects still exist in
the calibrations at the level of a few percent. Our InfraRed Flux Method
temperature scale is 100K hotter than recent analogous determinations in the
literature, but is in agreement with spectroscopically calibrated temperature
scales and fits well the colours of the Sun. Our angular diameters are
typically 3% smaller when compared to other (indirect) determinations of
angular diameter for such stars, but are consistent with the limb-darkening
corrected predictions of the latest 3D model atmospheres and also with the
results of asteroseismology. Very tight empirical relations are derived for
bolometric luminosity, effective temperature and angular diameter from
photometric indices. We find that much of the discrepancy with other
temperature scales and the uncertainties in the infrared synthetic colours
arise from the uncertainties in the use of Vega as the flux calibrator. Angular
diameter measurements for a well chosen set of G and K dwarfs would go a long
way to addressing this problem.Comment: 34 pages, 20 figures. Accepted by MNRAS. Landscape table available
online at http://users.utu.fi/luccas/IRFM
Numerical invariants of Fano 4-folds
Let X be a (smooth, complex) Fano 4-fold. For any prime divisor D in X,
consider the image of N_1(D) in N_1(X) under the push-forward of 1-cycles, and
let c_D be its codimension in N_1(X). We define an integral invariant c_X of X
as the maximal c_D, where D varies among all prime divisors in X. One easily
sees that c_X is at most rho_X-1 (where rho is the Picard number), and that c_X
is greater or equal than rho_X-rho_D, for any prime divisor D in X. We know
from previous works that if c_X > 2, then either X is a product of Del Pezzo
surfaces and rho_X is at most 18, or c_X=3 and rho_X is at most 6. In this
paper we show that if c_X=2, then rho_X is at most 12.Comment: 11 page
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