Stability of Genus Five Canonical Curves
نویسنده
چکیده
We analyze GIT stability of nets of quadrics in P4 up to projective equivalence. Since a general net of quadrics defines a canonically embedded smooth curve of genus 5, the resulting quotient M G := G(3, 15)ss//SL(5) gives a birational model of M5. We study the geometry of the associated contraction f : M5 99K M G , and prove that f is the final step in the log minimal model program for M5.
منابع مشابه
The Tangent Cones at Double points of Prym-Canonical Divisors of Curves of genus 7
Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...
متن کاملQuadric Rank Loci on Moduli of Curves and K3 Surfaces
Assuming that φ : Sym(E) → F is a morphism of vector bundles on a variety X, we compute the class of the locus in X where Ker(φ) contains a quadric of prescribed rank. Our formulas have many applications to moduli theory: (i) we find a simple proof of Borcherds’ result that the Hodge class on the moduli space of polarized K3 surfaces of fixed genus is of Noether-Lefschetz type, (ii) we construc...
متن کاملGeometric Invariant Theory of Syzygies, with Applications to Moduli Spaces
We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, a...
متن کاملCanonical Correlation Analysis for Determination of Relationship between Morphological and Physiological Pollinated Characteristics in Five Varieties of Phalaenopsis
Phalaenopsis is an important genus of orchids that is grown for economical production of cut flower and potted plants. The objective of this study is the evaluation of correlation between morphological and physiological traits of self and cross-pollination of 5 varieties of Phalaenopsis orchid. Some morphological traits were measured: Capsule length (CL), capsule volume (CV), weight of seeds in...
متن کاملStability of Tails and 4-canonical Models
We show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus g ≥ 3 are the moduli space M ps g of pseudo-stable curves constructed by Schubert in [7] using Chow varieties and 3-canonical models. The only new ingredient needed in the Hilbert scheme variant is a more careful analysis of the stability with respect to a certain 1-ps λ of ...
متن کامل