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The k-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface X corresponds to a regular unimodular trian-gulation D of the polytope definin...
For m 2 N,m  1, we determine the irreducible components of the m − th jet scheme of a toric surface S. For m big enough, we connect the number of a class of these irreducible components to the...
The Severi variety parameterizes plane curves of degree d with  nodes.Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of CP2....

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