Quadric Hypersurfaces Containing a Projectively Normal Curve

2005 ◽  
Vol 12 (2) ◽  
pp. 201-206
Author(s):  
Edoardo Ballico ◽  
Changho Keem
Keyword(s):  
Line Bundles ◽  
Normal Curve ◽  
Connected Component ◽  
Base Locus

Abstract Let 𝐶 ⊂ 𝐏𝑛 be a smooth projectively normal curve. Let 𝑍 be the scheme-theoretic base locus of 𝐻0(𝐏𝑛, 𝐼𝐶(2)) and 𝑍′ the connected component of 𝑍 containing 𝐶. Here we show that 𝑍′ = 𝐶 in certain cases (e.g., non-special line bundles with degree near to 2𝑝𝑎 (𝐶)–2 or certain special line bundles on general 𝑘-gonal curves).

scholarly journals On the non-divisorial base locus of big and nef line bundles on K3[2]-type varieties

2020 ◽  
pp. 1-27
Author(s):  
Ulrike Rieß
Keyword(s):  
Moduli Spaces ◽  
Hilbert Scheme ◽  
Ample Line Bundle ◽  
Base Point ◽  
K3 Surfaces ◽  
Line Bundles ◽  
Codimension Two ◽  
Base Locus ◽  
Base Loci ◽  
Symplectic Varieties

Abstract We approach non-divisorial base loci of big and nef line bundles on irreducible symplectic varieties. While for K3 surfaces, only divisorial base loci can occur, nothing was known about the behaviour of non-divisorial base loci for more general irreducible symplectic varieties. We determine the base loci of all big and nef line bundles on the Hilbert scheme of two points on very general K3 surfaces of genus two and on their birational models. Remarkably, we find an ample line bundle with a non-trivial base locus in codimension two. We deduce that, generically in the moduli spaces of polarized K3[2]-type varieties, the polarization is base point free.

scholarly journals Bigq-ample line bundles

2012 ◽  
Vol 148 (3) ◽  
pp. 790-798 ◽  
Author(s):  
Morgan V. Brown
Keyword(s):  
Line Bundle ◽  
Coherent Sheaf ◽  
Line Bundles ◽  
Base Locus ◽  
Codimension One ◽  
Projective Scheme ◽  
Complex Projective

AbstractA recent paper of Totaro developed a theory ofq-ample bundles in characteristic 0. Specifically, a line bundleLonXisq-ample if for every coherent sheaf ℱ onX, there exists an integerm0such thatm≥m0impliesHi(X,ℱ⊗𝒪(mL))=0 fori>q. We show that a line bundleLon a complex projective schemeXisq-ample if and only if the restriction ofLto its augmented base locus isq-ample. In particular, whenXis a variety andLis big but fails to beq-ample, then there exists a codimension-one subschemeDofXsuch that the restriction ofLtoDis notq-ample.

scholarly journals THE GAMMA CONSTRUCTION AND ASYMPTOTIC INVARIANTS OF LINE BUNDLES OVER ARBITRARY FIELDS

2019 ◽  
pp. 1-43 ◽  
Author(s):  
TAKUMI MURAYAMA
Keyword(s):  
Line Bundles ◽  
Ground Field ◽  
Projective Varieties ◽  
Base Locus ◽  
Asymptotic Invariants ◽  
Complex Projective ◽  
Theoretic Version ◽  
Do So

We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of Hochster and Huneke to reduce to the setting where the ground field is $F$ -finite. Our main result uses the gamma construction to extend the ampleness criterion of de Fernex, Küronya, and Lazarsfeld using asymptotic cohomological functions to projective varieties over arbitrary fields, which was previously known only for complex projective varieties. We also extend Nakayama’s description of the restricted base locus to klt or strongly $F$ -regular varieties over arbitrary fields.

scholarly journals Fourier–Mukai and autoduality for compactified Jacobians. I

2019 ◽  
Vol 2019 (755) ◽  
pp. 1-65 ◽  
Author(s):  
Margarida Melo ◽  
Antonio Rapagnetta ◽  
Filippo Viviani
Keyword(s):  
Derived Category ◽  
Line Bundles ◽  
Higgs Bundles ◽  
Connected Component ◽  
Generalized Jacobian ◽  
Langlands Duality ◽  
Integral Curves ◽  
Numerical Equivalence ◽  
Algebraic Equivalence ◽  
Compactified Jacobian

AbstractTo every singular reduced projective curve X one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian of X. We prove that, for a reduced curve with locally planar singularities, the integral (or Fourier–Mukai) transform with kernel the Poincaré sheaf from the derived category of the generalized Jacobian of X to the derived category of any fine compactified Jacobian of X is fully faithful, generalizing a previous result of Arinkin in the case of integral curves. As a consequence, we prove that there is a canonical isomorphism (called autoduality) between the generalized Jacobian of X and the connected component of the identity of the Picard scheme of any fine compactified Jacobian of X and that algebraic equivalence and numerical equivalence of line bundles coincide on any fine compactified Jacobian, generalizing previous results of Arinkin, Esteves, Gagné, Kleiman, Rocha, and Sawon.The paper contains an Appendix in which we explain how our work can be interpreted in view of the Langlands duality for the Higgs bundles as proposed by Donagi–Pantev.

The Normal Curve and its Abnormalities

1969 ◽  
Vol 14 (1) ◽  
pp. 10-11
Author(s):  
ERNEST G. POSER
Keyword(s):  
Normal Curve

The Subnormal Area Under the Normal Curve of Intelligence

1968 ◽  
Vol 13 (1) ◽  
pp. 19-21
Author(s):  
PAUL R. DOKECKI
Keyword(s):  
Normal Curve
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