【115/6/29】9:00-10:00 顏瑜廷 同學（國立成功大學數學系)
發佈日期 :
2026-06-23
| Student Seminar on Geometry | |
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| Time | 2026-6-29 9:00-10:00 |
| Venue | 數學館2樓 31203 教室 |
| Speaker | 顏瑜廷 同學（國立成功大學數學系) |
| Title | Riemann-Roch on Toric Surfaces and Lattice Polygons |
| Abstract | This presentation explores the intersection of algebraic geometry and discrete combinatorics through the lens of smooth complete toric surfaces. We will review the Riemann-Roch theorem for surfaces alongside Noether's theorem, demonstrating how Demazure vanishing simplifies these topological and algebraic invariants. Furthermore, we will establish a direct correspondence between these cohomological dimensions and the geometry of lattice polygons via Ehrhart polynomials. Finally, we will apply this framework to derive the sectional genus of associated curves and prove that the sum of boundary lattice points for any two-dimensional reflexive polygon and its dual is exactly 12. |
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| Organizer | 賴青瑞、李宗儒 |
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