Geometric Invariant Theory of Syzygies, with Applications to Moduli Spaces
نویسنده
چکیده
We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.
منابع مشابه
Anomaly Matching and Syzygies in N =1 Gauge Theories
We investigate the connection between the moduli space of N = 1 supersymmetric gauge theories and the set of polynomial gauge invariants constrained by classical/quantum relations called syzygies. We examine the existence of a superpotential reproducing these syzygies and the link with the 't Hooft anomaly matching between the fundamental fields at high energy and the gauge invariant degrees of...
متن کاملGood Moduli Spaces for Artin Stacks
We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford’s geometric invariant theory and tame stacks.
متن کاملOn Atkin-Lehner correspondences on Siegel spaces
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime l...
متن کاملA Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps
We construct the moduli spaces of stable maps, Mg,n(P , d), via geometric invariant theory. This construction is only valid over Spec C, but a special case is a GIT presentation of the moduli space of stable curves of genus g with n marked points, Mg,n; this is valid over any base field. Our method follows that used in the case n = 0 by Gieseker in [6], to construct Mg, though our proof that th...
متن کاملRelations among Fixed Points
Let M be a smooth manifold with a circle action, and {P } be the fixed point sets. The problem I want to discuss in this paper is how to get the topological information of one relatively complicated fixed point set, say P 0 , from the other much simpler fixed points. Such problems are interesting in symplectic geometry and geometric invariant theory, especially in the study of moduli spaces. In...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017