منابع مشابه
The Hilbert Scheme
Many important moduli spaces can be constructed as quotients of the Hilbert scheme by a group action. For example, to construct the moduli space of smooth curves of genus g ≥ 2, we can first embed all smooth curves of genus g in Pn(2g−2)−g by a sufficiently large multiple of their canonical bundle K C . Any automorphism of a variety preserves the canonical bundle. Hence, two n-canonically embed...
متن کاملThe Full Flag Hilbert Scheme of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve.
We study the relative full-flag Hilbert scheme of a family of curves, parameterizing chains of subschemes, containing a node. We will prove that the relative full flag Hilbert scheme is normal with locally complete intersection singularities. We also study the Hilbert scheme of points of the cusp curve and show the punctual Hilbert scheme is isomorphic to P. We will see the Hilbert scheme has o...
متن کاملQuestions of Connectedness of the Hilbert Scheme
We review the present state of the problem, for each degree d and genus g , is the Hilbert scheme of locally Cohen–Macaulay curves in P 3 connected?
متن کاملCombinatorics of the Toric Hilbert Scheme
The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2016
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201407_003