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A bound on the degree of schemes defined by quadratic equations
-
Alberto Alzati
und
José Carlos Sierra
Veröffentlicht/Copyright:
29. Juni 2012
Abstract.
We consider complex projective schemes 
defined
by quadratic equations and satisfying a technical hypothesis on the
fibres of the rational map associated to the linear system of
quadrics defining X. Our assumption is related to the syzygies of
the defining equations and, in particular, it is weaker than
properties N2, 
and K2. In this setting, we show that
the degree d of is bounded by a function
of its codimension c, whose asymptotic behavior is given by
, thus improving the obvious bound 
. More precisely, we get the bound
. Furthermore, if X satisfies
property 
or 
, we obtain the better bound
. Some classification
results are also given when equality holds.
Received: 2009-11-10
Revised: 2010-06-21
Published Online: 2012-06-29
Published in Print: 2012-07-01
© 2012 by Walter de Gruyter Berlin Boston
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Schlagwörter für diesen Artikel
Varieties defined by quadrics;
2-Veronese embeddings;
apparent double points;
syzygies
Artikel in diesem Heft
- Masthead
- Representations of quivers over a ring and the Weak Krull–Schmidt Theorems
- Logarithmically improved regularity criteria for the 3D viscous MHD equations
- Tilting modules and universal localization
- A bound on the degree of schemes defined by quadratic equations
- Hardy's inequality in the scope of Dirichlet forms
- On some Banach spaces of martingales associated with function spaces
- Construction of quasi-periodic response solutions in forced strongly dissipative systems
- On the description of Leibniz superalgebras of nilindex
- Presentations of graph braid groups
- On the vanishing of the lower K-theory of the holomorph of a free group on two generators
- Boundedly generated subgroups of finite groups
