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A bound on the degree of schemes defined by quadratic equations
-
Alberto Alzati
and
José Carlos Sierra
Published/Copyright:
June 29, 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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Keywords for this article
Varieties defined by quadrics;
2-Veronese embeddings;
apparent double points;
syzygies
Articles in the same Issue
- 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
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- Construction of quasi-periodic response solutions in forced strongly dissipative systems
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