Hi all,

I am a second year math PhD student at Florida State University studying 
algebraic geometry. Last year I had the chance to work on Sage through GSoC 
and implemented basic functionality for algebraic curves. During the course 
of that project I came across some generic algebraic geometry functionality 
that I think would be nice to have in Sage, including more support for 
general schemes (in order to handle gluing) and blow ups for schemes via 
the Rees algebra construction.

I'd love to have the opportunity to participate in GSoC a second time and 
have been working on a project proposal for this year to implement an 
assortment of general algebraic geometry functionality, most of which in 
the direction of what Magma currently offers that's not yet in Sage. In 
addition to the above topics, some other goals I've been investigating for 
this project include implementing basic support for working with algebraic 
surfaces such as parameterization/implicitization (at least for certain 
special types of rational surfaces), and more functionality for projecting 
projective schemes to subspaces. I have discussed potential mentorship for 
such a project with Benjamin Hutz, but it would help a lot to have another 
mentor if possible.

Would anyone be interested in mentoring an algebraic geometry focused 
project like this? I'm currently investigating potential additional topics 
to add to the proposal, but I lack the expertise in some areas such as 
toric varieties to determine what kinds of functionality there might be 
desirable/feasible to implement in Sage. I would be very grateful for any 
guidance or topic suggestions.

Thank you,
Grayson

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