A wall-crossing formula for degrees of Real central projections

作者：Okonek Christian; Teleman Andrei^*

来源：International Journal of Mathematics, 2014, 25(4): 14500384.

DOI：10.1142/14500384X14500384

• Real projective variety
• degree
• central projection
• relative orientation
• wallcrossing
• conservation of numbers

The main result is a wall-crossing formula for central projections defined on submanifolds of a Real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to Real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a Z-valued degree map in a coherent way. We end the article with several examples, e. g. the pole placement map associated with a quotient, the Wronski map, and a new version of the Real subspace problem.

• 出版日期2014-4