Download PDF by Alexander Polishchuk: Abelian varieties and the Fourier transform

By Alexander Polishchuk

The purpose of this ebook is to provide a contemporary therapy of the idea of theta features within the context of algebraic geometry. the newness of its strategy lies within the systematic use of the Fourier-Mukai rework. the writer starts off by means of discussing the classical concept of theta services from the perspective of the illustration conception of the Heisenberg workforce (in which the standard Fourier remodel performs the in demand role). He then indicates that during the algebraic method of this thought, the Fourier–Mukai remodel can frequently be used to simplify the present proofs or to supply thoroughly new proofs of many very important theorems. Graduate scholars and researchers with powerful curiosity in algebraic geometry will locate a lot of curiosity during this quantity.

Show description

Read Online or Download Abelian varieties and the Fourier transform PDF

Best algebraic geometry books

Download e-book for kindle: Algebraic cycles and Hodge theory: lectures given at the 2nd by Mark L. Green, Jacob P. Murre, Claire Voisin, Alberto

The most target of the CIME summer time tuition on "Algebraic Cycles and Hodge thought" has been to assemble the main energetic mathematicians during this zone to make the purpose at the current state-of-the-art. therefore the papers integrated within the court cases are surveys and notes at the most crucial issues of this region of study.

Resolution of Singularities of Embedded Algebraic Surfaces - download pdf or read online

This re-creation describes the geometric a part of the author's 1965 evidence of desingularization of algebraic surfaces and solids in nonzero attribute. The e-book additionally presents a self-contained advent to birational algebraic geometry, dependent simply on uncomplicated commutative algebra. furthermore, it supplies a brief facts of analytic desingularization in attribute 0 for any measurement present in 1996 and in response to a brand new avatar of an algorithmic trick hired within the unique variation of the ebook.

Read e-book online Knots and physics PDF

This quantity presents an creation to knot and hyperlink invariants as generalized amplitudes for a quasi-physical procedure. The calls for of knot concept, coupled with a quantum-statistical framework, create a context that clearly features a diversity of interrelated issues in topology and mathematical physics.

Additional info for Abelian varieties and the Fourier transform

Example text

3]). m; n/ and rank m C n, with discriminant lattice AL . L/ denote the minimal number of generators of AL . L/ Ä m C n 2, then any other lattice with the same rank, signature and discriminant lattice is isomorphic to L. Overlattices Now assume that L and M are two even lattices of the same rank, such that L embeds inside of M. Then we say that M is an overlattice of L. If we begin with a lattice M, then it is easy to compute all possible sublattices of maximal rank of L, but the problem of computing all possible overlattices of L is more subtle.

One may check that for a general choice of a; b; c, the discriminant vanishes simply at four other points in P1 , giving four further singular fibres of type I1 . 1/ D 24, as expected. For a singular fibre of type II , the root lattice Rp is isomorphic to . E8 /. Therefore, the lattice L for this K3 surface is isomorphic to H ˚ . E8 / ˚ . E8 / (recall that singular fibres of type I1 are irreducible, so do not contribute to L ). S; /tors is trivial, so Corollary 2 shows that S is in fact H ˚ . E8 / ˚ .

J. 116, 1–15 (1989) 35. : Abelian varieties attached to polarized K3 -surfaces. Math. Ann. 169, 239–242 (1967) 36. : Degenerations of K3 surfaces and Enriques surfaces. Math. USSR Izv. 11(5), 957–989 (1977) 37. : On modifications of degenerations of surfaces with Ä D 0. Math. USSR Izv. 17(2), 339–342 (1981) 38. : On minimally elliptic singularities. Am. J. Math. 99(6), 1257–1295 (1977) 42 A. Harder and A. Thompson 39. : The KSBA compactification for the moduli space of degree two K3 pairs (2012, preprint).

Download PDF sample

Abelian varieties and the Fourier transform by Alexander Polishchuk


by Charles
4.0

Rated 4.41 of 5 – based on 48 votes