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Generalized Hitchin systems on rational surfaces

Rains, Eric M. (2013) Generalized Hitchin systems on rational surfaces. , Pasadena, CA. (Submitted)

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By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of difference equations on an elliptic curve (arising in the theory of elliptic special functions). The common feature of the relaxations is that they can be identified with moduli spaces of sheaves on rational surfaces. Not only does this make various natural questions become purely geometric (rigid equations correspond to -2-curves), it also establishes a number of nontrivial correspondences between different moduli spaces, since a given moduli space of sheaves is typically the relaxation of infinitely many moduli spaces of equations. In the process of understanding this, we also consider a number of purely geometric questions about rational surfaces with anticanonical curves; e.g., we give an essentially combinatorial algorithm for testing whether a given divisor is the class of a -2-curve or is effective with generically integral representative.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20170922-142713387
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81767
Deposited By: Tony Diaz
Deposited On:22 Sep 2017 22:07
Last Modified:03 Oct 2019 18:46

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