By R.K. Lazarsfeld
Quantity paintings containing a modern account on "Positivity in Algebraic Geometry".
Both volumes additionally to be had as hardcover variations as Vols. forty eight and forty nine within the sequence "Ergebnisse der Mathematik und ihrer Grenzgebiete".
A good buy of the cloth has no longer formerly seemed in booklet form.
Volume II is extra on the study level and a bit extra really good than quantity I.
Volume II features a survey of positivity for vector bundles, and strikes directly to a scientific improvement of the speculation of multiplier beliefs and their applications.
Contains many concrete examples, purposes, and tips that could additional developments
Read Online or Download Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals PDF
Similar algebraic geometry books
Backbone name: advent to moduli difficulties and orbit areas.
Higher-Dimensional Algebraic Geometry experiences the category concept of algebraic types. This very lively sector of study continues to be constructing, yet an awesome volume of data has collected over the last two decades. The author's objective is to supply an simply obtainable advent to the topic.
Now in new alternate paper versions, those vintage biographies of 2 of the best twentieth Century mathematicians are being published less than the Copernicus imprint. those noteworthy money owed of the lives of David Hilbert and Richard Courant are heavily similar: Courant's tale is, in lots of methods, visible because the sequel to the tale of Hilbert.
That includes a mix of unique study papers and entire surveys from a world staff of prime researchers within the thriving fields of foliation thought, holomorphic foliations, and birational geometry, this ebook provides the court cases of the convention "Foliation thought in Algebraic Geometry," hosted by way of the Simons origin in big apple urban in September 2013.
- Global Aspects of Complex Geometry
- Fourier-Mukai Transforms in Algebraic Geometry
- Real Algebraic Geometry and Topology: A Conference on Real Algebraic Geometry and Topology, December 17-21, 1993, Michigan State University
- The Möbius Strip: Dr. August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology
Extra resources for Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals
Bogomolov’s construction). Let Y1 , . . , Ym be smooth projective varieties of dimension d ≥ 1, each having big cotangent bundle, 9 and let X ⊆ Y1 × . . × Ym be a general complete intersection of very ample divisors. Bogomolov proves that if d(m + 1) dim X ≤ , 2d + 1 then X has ample cotangent bundle. Bogomolov and Debarre deduce from this that there exists a projective variety X having ample cotangent bundle with the additional property that π1 (X) is any group arising as the fundamental group of a smooth projective variety: in particular, X can be simply connected.
3 Examples and Constructions In order to add substance to the general theory, we present in this section several examples and constructions of ample and nef vector bundles. Our hope is to convey a sense of some of the many settings in which positivity of bundles arises “in nature”, and to illustrate a few of the methods that have been used to detect and exploit it. In the first two subsections, we discuss the geometric consequences of positivity conditions on tangent, cotangent and normal bundles.
1] proves in the situation of the Proposition that the formal cohomology groups H i M , E are finite dimensional for all i < d. 5] that if in addition M is projective, then for every coherent sheaf F on M , the cohomology group H i M − X, F is finite dimensional whenever i ≥ n−d. There have been a number of attempts to find global geometric consequences of the amplitude of the normal bundle N = NX/M . 30). 5] concerning what one might expect in higher codimension: Hartshorne’s Conjecture A. If X ⊆ M is a smooth subvariety with ample normal bundle, then a sufficiently high multiple of [X] should move (as a cycle) in a large algebraic family.
Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals by R.K. Lazarsfeld
Categories: Algebraic Geometry