smooth compactification
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2019 ◽  
Vol 29 (01) ◽  
pp. 9-21
Author(s):  
André L. Meireles Araújo ◽  
José Alberto Maia ◽  
Fernando Xavier

We know from a result due to Noether–Lefschetz that a very general surface of degree at least 4 in [Formula: see text] contains only curves which are complete intersections with other surfaces. The main goal of this paper is to construct an explicit and smooth compactification of a parameter space for surfaces in [Formula: see text] of degree [Formula: see text] for all sufficiently large [Formula: see text], containing one conic and one line. The construction also applies to surfaces in [Formula: see text] containing one plane curve and one line. As an application, we compute the degree of the locus of surfaces of degree [Formula: see text] containing one conic and one line.


2016 ◽  
Vol 56 (1) ◽  
pp. 165-175
Author(s):  
Indranil Biswas ◽  
S. Senthamarai Kannan ◽  
D. S. Nagaraj

2014 ◽  
Vol 158 (1) ◽  
pp. 131-145 ◽  
Author(s):  
ARNE SMEETS

AbstractLetkbe a number field andTak-torus. Consider a family of torsors underT, i.e. a morphismf:X→ ℙ1kfrom a projective, smoothk-varietyXto ℙ1k, the generic fibreXη→ η of which is a smooth compactification of a principal homogeneous space underT⊗kη. We study the Brauer–Manin obstruction to the Hasse principle and to weak approximation forX, assuming Schinzel's hypothesis. We generalise Wei's recent results [21]. Our results are unconditional ifk=Qand all non-split fibres offare defined overQ. We also establish an unconditional analogue of our main result for zero-cycles of degree 1.


2003 ◽  
Vol 568 (3-4) ◽  
pp. 261-269 ◽  
Author(s):  
S. Cucu ◽  
H. Lü ◽  
J.F. Vázquez-Poritz

2002 ◽  
Vol 91 (2) ◽  
pp. 221 ◽  
Author(s):  
I. Vainsencher ◽  
F. Xavier

We give an elementary, explicit smooth compactification of a parameter space for the family of twisted cubics. The construction also applies to the family of subschemes defined by determinantal nets of quadrics, e.g., cubic ruled surfaces in $\boldsymbol P^4$, Segre varieties in $\boldsymbol P^5$. It is suitable for applications of Bott's formula to a few enumerative problems.


1996 ◽  
Vol 141 ◽  
pp. 107-124 ◽  
Author(s):  
Claude Sabbah

Let U be a smooth quasi-projective variety over C and let f be a regular function on U. Let DU be the sheaf of algebraic differential operators on U and let M be a regular holonomic DU-module: here, regular means that there exists some smooth compactification X of U and some extension of M as a DX-module which is regular holonomic on X (one also may avoid the use of a smooth compactification to define regularity, see [17]).


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