Jet Schemes and Singularities of W d r (C) Loci

@article{Zhu2012JetSA,
  title={Jet Schemes and Singularities of W d r (C) Loci},
  author={Z. Zhu},
  journal={Communications in Algebra},
  year={2012},
  volume={43},
  pages={3134 - 3159}
}
  • Z. Zhu
  • Published 2012
  • Mathematics
  • Communications in Algebra
Kempf proved that the theta divisor of a smooth projective curve C has rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular, we recover Kempf's theorem in this way. For general projective smooth curves, our method also gives a formula for the log canonical threshold of the pair . 
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References

SHOWING 1-10 OF 20 REFERENCES
Jet schemes of locally complete intersection canonical singularities
We prove that if X is a locally complete intersection variety, then X has all the jet schemes irreducible if and only if X has canonical singularities. After embedding X in a smooth variety Y, we useExpand
Singularities of theta divisors and the birational geometry of irregular varieties
The purpose of this paper is to show how the generic vanishing theorems of M. Green and the second author can be used to settle several questions and conjectures concerning the geometry of irregularExpand
Arcs on determinantal varieties
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to computeExpand
Singularities of pairs via jet schemes
Let X be a smooth variety and Y a closed subscheme of X. By comparing motivic integrals on X and on a log resolution of (X,Y), we prove the following formula for the log canonical threshold of (X,Y):Expand
Lectures on curves on an algebraic surface
These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined overExpand
On the Geometry of a Theorem of Riemann
Let C be a smooth complete algebraic curve. Let I: C-+J be an universal abelian integral of C into its Jacobian J. Furthermore, let I(i): C(i) J be the mapping sending a point c1 + *-+ ci in the ithExpand
Jet schemes, log discrepancies and inversion of adjunction
Singularities play a key role in the Minimal Model Program. In this paper we show how some of the open problems in this area can be approached using jet schemes. Let (X, Y ) be a pair, where X is aExpand
Geometry of algebraic curves
Preface.- Guide to the Reader.- Chapter IX. The Hilbert Scheme.- Chapter X. Nodal curves.- Chapter XI. Elementary deformation theory and some applications.- Chapter XII. The moduli space of stableExpand
Algebraic Geometry
Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)
Positivity for vector bundles, and multiplier ideals
Notation and Conventions.- Two: Positivity for Vector Bundles.- 6 Ample and Nef Vector Bundles.- 6.1 Classical Theory.- 6.1.A Definition and First Properties.- 6.1.B Cohomological Properties.- 6.1.CExpand
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