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Titlebook: Geometric Invariant Theory for Polarized Curves; Gilberto Bini,Fabio Felici,Filippo Viviani Book 2014 Springer International Publishing Sw

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A Criterion of Stability for Tails,In this chapter we would like to state a criterion of stability for tails based on the Hilbert-Mumford criterion and on the parabolic group. Let . with . > 2(2. − 2), where . is the union of two curves .. and .. (of degrees .., .. and genus .., ..) that intersect each other transversally in a single point ..
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Semistable, Polystable and Stable Points (Part I),The aim of this chapter is to describe the points of Hilb. that are Hilbert or Chow semistable, polystable and stable for . The range . will be investigated later.
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Stability of Elliptic Tails,In this chapter, we will use the criterion of stability for tails (Proposition .) in order to study the stability of elliptic curves for .. We notice that in this range—by the basic inequality (.)—it suffices to consider the elliptic curves of degree 4.
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Extra Components of the GIT Quotient,So far, we have considered the action of . over Hilb., and we have restricted our attention to . and ., the Chow or Hilbert semistable loci consisting of connected curves. It is very natural to ask if there are Chow or Hilbert semistable points . with . not connected. In this chapter we will answer this question.
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