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Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
2015/12/17
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
THE GEOMETRIC THETA CORRESPONDENCE FOR HILBERT MODULAR SURFACES
GEOMETRIC THETA CORRESPONDENCE；HILBERT MODULAR SURFACES
2015/10/14
In a series of papers [11, 12, 13, 14] we have been studying the geometric theta correspondence (see below) for non-compact arithmetic quotients of symmetric spaces associated to orthogonal groups. It...
Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
Horocyclic Flows Complete Hyperbolic Surfaces Finite Area
2015/8/26
We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution ...
Configuration types and cubic surfaces
Fat points free resolution cubic surface matroid Hilbert function
2012/4/16
This paper is a sequel to the paper \cite{refGH}. We relate the matroid notion of a combinatorial geometry to a generalization which we call a configuration type. Configuration types arise when one cl...
Stability of tautological bundles on the degree two Hilbert scheme of surfaces
moduli spaces irreducible holomorphic symplectic manifolds K3 surfaces
2012/3/1
Let (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In t...
Cyclic groups of automorphisms of complex K3 surfaces
Cyclic groups automorphisms complex K3 surfaces
2012/2/29
We determine all possible orders of automorphisms of complex K3 surfaces. A positive integer N is the order of an automorphism of a complex K3 surface if and only if \phi(N) \leq 20 and N is not 60, w...
Beauville surfaces, moduli spaces and finite groups
Beauville surfaces moduli spaces finite groups Algebraic Geometry
2011/9/22
Abstract: In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with...
Computing the Singularities of Rational Surfaces
Singularities of Rational Surfaces Algebraic Geometry
2011/9/21
Abstract: Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $...
On the existence of curves with $A_k$-singularities on $K3$-surfaces
versal deformations tacnodes Severi varieties K3 surfaces Ak-singularities
2011/9/19
Abstract: Let $(S,H)$ be a general primitively polarized $K3$ surface. We prove the existence of curves in $|\mathcal O_S(nH)|$ with $A_k$-singularities and corresponding to regular points of the equi...
The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
Kummer surfaces Mathieu group High Energy Physics - Theory Algebraic Geometry
2011/10/9
Abstract: We construct a bijection between the full integral homology lattice of K3 and a Niemeier lattice, which is simultaneously compatible with the finite symplectic automorphism groups of several...
Abstract: We give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divi...
Exceptional bundles associated to degenerations of surfaces
Exceptional bundles degenerations of surfaces Algebraic Geometry
2011/9/5
Abstract: In 1981 J. Wahl described smoothings of surface quotient singularities with no vanishing cycles. Given a smoothing of a projective surface X of this type, we construct an associated exceptio...
A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces
ideal sheaf Fourier-Mukai divisor abelian surface Hilbert scheme stable sheaf
2011/9/5
Abstract: We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such shea...
A note on exceptional unimodal singularities and K3 surfaces
exceptional unimodal singularities K3 surfaces note Algebraic Geometry
2011/9/1
Abstract: This is a short note on the relation between the graded stable derived categories of 14 exceptional unimodal singularities and the derived category of K3 surfaces obtained as compactificatio...