656 research outputs found
Boundedness for surfaces in weighted P^4
Ellingsrud and Peskine (1989) proved that there exists a bound on the degree
of smooth non general type surfaces in P^4. The latest proven bound is 52 by
Decker and Schreyer in 2000.
In this paper we consider bounds on the degree of a quasismooth non-general
type surface in weighted projective 4-space. We show that such a bound in terms
of the weights exists, and compute an explicit bound in simple cases
Abelianisation of orthogonal groups and the fundamental group of modular varieties
We study the commutator subgroup of integral orthogonal groups belonging to
indefinite quadratic forms. We show that the index of this commutator is 2 for
many groups that occur in the construction of moduli spaces in algebraic
geometry, in particular the moduli of K3 surfaces. We give applications to
modular forms and to computing the fundamental groups of some moduli spaces
Moduli spaces of polarised symplectic O'Grady varieties and Borcherds products
We study moduli spaces of O'Grady's ten-dimensional irreducible symplectic
manifolds. These moduli spaces are covers of modular varieties of dimension 21,
namely quotients of hermitian symmetric domains by a suitable arithmetic group.
The interesting and new aspect of this case is that the group in question is
strictly bigger than the stable orthogonal group. This makes it different from
both the K3 and the K3^[n] case, which are of dimension 19 and 20 respectively
Moduli spaces of irreducible symplectic manifolds
We study the moduli spaces of polarised irreducible symplectic manifolds. By
a comparison with locally symmetric varieties of orthogonal type of dimension
20, we show that the moduli space of 2d polarised (split type) symplectic
manifolds which are deformation equivalent to degree 2 Hilbert schemes of a K3
surface is of general type if d is at least 12.Comment: Exposition improved, Reference to work of Debarre and Voisin added,
Corollary 1.6 remove
Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups
Given a group automorphism , one has an action of
on itself by -twisted conjugacy, namely, .
The orbits of this action are called -conjugacy classes. One says that
has the -property if there are infinitely many
-conjugacy classes for every automorphism of . In this
paper we show that any irreducible lattice in a connected semi simple Lie group
having finite centre and rank at least 2 has the -property.Comment: 6 page
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